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Correspondence, 1991-2000

Material Information

Title:
Correspondence, 1991-2000
Physical Description:
Unknown
Physical Location:
 Box: 1 Folder: Correspondence, 1991-2000

Subjects

Subjects / Keywords:
Mathematics -- History -- 20th century

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
System ID:
AA00007262:00001

Full Text

Systems Engineering
Member Technical Staff
11717 Exploration Lane
Germantown, MD 20874, U.S.A.
Tel: (301) 428-7169
TWX: (710) 828-0541
FAX: (301) 428-1868/2830

HUGHES
NETWORK SYSTEMS

Subsidiary of
Hughes Aircraft Company

1900 South Eads St. Apt 417
Arlington VA 22202

H: (703) 892 2467
0: (301) 428 7169

Professor K. L. Chung
Department of Mathematics
Stanford University
Stanford CA, 94305 Feb. 15 1991

It was a great honor and pleasure for me to talk to you, a world well konwn great

mathematician scholar. I am unable to explain in words how deeply I am touched

and honored by my conversation with you a great scholar.

time any longer and mention that along with this letter I have enclosed a check

for the amount you indicated. I would greatly appreciate if you would please

kindly mail the text to my home address given above. I again would like to

thank you for the honor you provided me by talking to me and having a copy of

your excellent text Markov Chains With Stationary Transition Probabilities ".

Thank you very much.

Very truly yours

Dear Prof. Chung:
I forwarded both the photo and the message to Federico Marchetti. I know he received your gifts
because he sent me a nice note just to say Hello and Thanks. He is very kind, as are most people
around here. On the other hand, I do feel like you about the somewhat extravagant prices one finds
in Italy. Housing is really a problem -and so is bureaucracy, by the way but people are on the
whole quite OK.
I see you have continued enjoying yourself while improving your Italian. I have not read
"Sagittario" by Ginzburg, but I did read Svevo's "Una Vita", also "Senilita'" and "La coscenza di
Zeno", which I enjoyed particularly. A few days ago I was listening to a very interesting radio
program called "De senectude", and they read a few lines from the very end of "Senilita'": it
brought back memories.
Incidently, listening to those programs on growing old has helped me to understand a few things
about aging. A nice and very revealing thought about the subject -which I heard in one of those
programs-goes more or less like this : It is not so much the image of ourselves on the mirror what
tells us about our getting old. It is not the greying, thinning hair or the vanishing freshness of our
skin. Instead, we learn that we are no longer young from the way the world reacts towards us: the
moment arrives when people no longer wonder about our promise for the future, but instead they
see us in the light of our past deeds (my own, free version).

I have a rather long backlog of reading material. The only thing I have been reading lately is
newspapers and similar. I mention the Gulf War, lots of work to do and little traveling time to get
to the University among my alibi, but it is all excuses really. You know what book I have just
bought and do intend to read?: "Pinocchio", by Collodio. I have never read the original version
and this may be a good occasion to do it. I remember I saw the film when I was a kid and I
enjoyed it greatly.
Talking about films, have you found anyone who can convert the "Il Sorpasso" videocassette from
the European to the American VHS format? I got it already -that was last November, before I
wrote my last letter- because I did not want to miss the chance (I don't think it should be easily
available). A new film I know you would certainly appreciate is "Nuovo Cinema Paradiso", by a
young fellow called Giuseppe Tomatore. It has met a great success everywhere and I liked it too.
Concerning Singapore: I never got any reply from them, after I sent out your letter. I figure that a
Department Head might feel happier if potential candidates for visiting positions use the more
conventional channels, and he/she might even fail to appreciate what he perceives as a friendly
imposition. So, a few weeks, ago I sent an e-mail in reply to an announcement by the National
University of Singapore which I saw in the latest issue of SIAM News. This time I did get a reply,
together with a regular application form. I do intend to fill it in and submit it, but not now. I want
to be serious, and I will not even apply when I know that I may have to teach a course for the
Statistics MSc students in Guanajuato during the first half of 1992. I will apply as soon as my
plans get definite. By the way, I have to indicate three references, would you be willing to be one
of them?
Besides reading I also like writing. Mathematical writing and also ordinary writing. Letter writing
is certainly a good pastime. Best regars from

Di ez-

STANFORD UNIVERSITY
STANFORD, CALIFORNA 94Za5
DERTMENT OF MHEMATICS
(415) 725Q424

Jan.
Dear zrof. Comtet:
A week ago I asked Song/Shiqi in Evry t
'To my surprise (and delight) I found th4
IAmma. Let Xk be lid with P(X1=t-l)=l/t
where b is an integer>l. Let Sn=Xl+...+xn.

P(SkO, l = P( ,, i Sbn = ) *so
Now the first probability above can be compd
No. 2C0 p.93 of your A. C. t. 1 (1970). [I
English book.] Thus I was able after all to
some 53 years ago by a combinatorial argument
P(SkO, l

bh-j h-|
The Lemr:,a was first "proved" experime,
a simple probability argument for it xas
ing is that the analogous lemma whenA
**W (b-as a), b>a. is atre trues. -1. 1
with the same proof. On the other hand, I a
resulting probability because the formula in
has no neat extension when (your) r is not a
checked with your reference there to Takacs,
The Lemma pf course is equivalent to a
ting problem (your minimum graph). I wonder
way by an extension of the reflection method
combinatorial proof of (*) please indicate a
H. W. Gould showed) it can be verified by Hag
once told me that he had a proof (not in his
what it is like. I am not familiar with the
With best wishes, Sincerel

3, 1993

forward a le
rectoryr.
following
P (X=-1))=(b-
Then

e paths for tl
sees 0 ce qu
d by the form
ave not seen
PROVE my form

ability in th

llys but the:
7 What may
ve is genera

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integer. I
ut that is n
identity in
f it can be
If there i
precise refer
's identity.
ook), but I a
literature, a

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me gene
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ur
a of

Lemma

I found
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ute the

e even
Be.
ount-
ved that
y other
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ohanty
ot sure
ou are.

22 avril, 19935 '

Monsieur Zheng Weian: (/ir'c Pr M eIuius4 g ,'

Je vais ecrire une petite histoire de cet "affaire ANONYM" (voir
le Post-s iptum dans mon memoirs Seminar 1988),\pour vous faire savoir
mon opinion de votre ancien matter M. en tant qu'il s'impose dans l'af-
faire bizarre. En y repensant, j'ai trouve des phrases justes chinoises
lesquelles decrient tres bien les choses [comme sont sages les chinois].
Pour 1'ANONYM sens nom e sans honneur:

Pour votre ancien maitre:

Si je n'avais connu ce dernier assez bien, j'aurais du adjouter

mais evidement ce n'etait qui lui appliquait. Nullegautres explica-
tions soient necessaire pour ce cretin anonyme: il ne savait rien ni
des travaux de Paul Levy, ni des remarques de moi, mais il avait l'au-
dackit de passer jugements sur tous les deux! C~est un type des gens,
surtout francais oui, qui conforme aux mot4chinois ecrits 111. Pour
leq second$mf4 on peut y mettere quelques details les voici. (1) M. m'a menti che il ne savait pas qui etais ce cretin, mais Neveu m'a inforep que en fait il avait etd lieu une petite conference drole, ct k a sur cet affaire, ~ M. participai*. Enfin, sal un peu les tra- vaux de Levy, n'est-ce pas? (2) Done, ha du savoir que c'est moi, pas 1'imbecile sans nom, |Ok avais raison pour tous les mathematiques en question. II mAa dit ya, en fait. Done) il pouvrait certainement dire ca sinon Qlu cretin meme (monsieur est tellement gentile.), alors a ce redacteur malinforme e stupid (un Herman ou Hermann, nom juif). Par exem le, il pouvrait dire: "Peut-etre CH. a fait des betises la [il ne m'a paye les compli- ments HABITUEL], mais toutefois il n'a pas tort et ne nuit en rien, no?" Des paroles pareilles suffiraient d'extraire d'embarras ,tout-le-monde: ~b'tho~nn'r 6eacte tti Q &hI oti 1 le cretin [d'apres Azema, c'est un A m d'aucun compete W le redacteur, le president Laurent Schwartz [qui m'a fait le compliment: "Parfait" apres ma conference], et ancore luimeme e moi. Mais non, ce monsieur ne stAt comme faire/ une chose si simple. Je me demand ancore: POURQUoI? (4) Enfin, ce qui imported pour les mathgmajiques plutot la +e politique francais, cJest que ni M. ni ses collaborateurSn'on'tjamais compris lidee original et plenipotente de Levy dans 1'invention de son temps locale. Ces gens-ci doivent done etudier, au serieux et avce beaucoup du htmilite ouil 1'exposition faite de moi et Balkdma qui est finalement parue dans Seminar 1990. Pour I commencer, je leur conseile vivement de rire, et re-rire, les remarques sur ce sujet dans ma conference di 22 juni, 1987, a Palaiseau. En tant que ces gens nM se consideraient.comme pareilles a ce cretin idiot etagaqant [parce que idiot, dunque agacantt] ils pouraient anoore, axxxxxxaIox quoique assez tardy, quelques choses nouvelles pour eux. Voici ancore une phrase just: *^V *34K 3 eur Zheng 'eian, je vais ecrire une petite histoire de c'affair "ANONYM centre Veritas" (voir mon article dans Seminar, 1988, le Postcritto), our vous faire savoir ce qui e passe alors avec votre maitre P-A A eyer et moi. En y repensant, j'ai le plaisir de trouver deux phrases chinoise qui descrient tres bien les choses --- que sages les chinoise! Jour 1'Anony m Pour votre maitre: Nulle explication n'est necessaire pour il premier: l'ignoto buffo [mots italians] mLx ne savail comprendre Paul Levy, mais il avait l'affronterie de dire "japonais". Pour le second, on doit y mettre cinq mots en su: (1) Meyer m.a menti che il ne savait rien de ce paure salaud sans nom e sand honneur; (2) Aleme si il n'aime pas mon article, il doive s'appercu che c'est moist non le sans-nom, chi avais raison pour les mathematiques che j'ai fait la recherche du temps (perdu), comme s'intitole l'ar- ticle. II pouvrait certainement le dire. sinon au salud meme, donc a ce redacteur ignorant (chi s'appel Herman ou Hermann). II peut dire ,par exernple: "C. a fait des betises la a mais toutefois, ca ne nuit a rien no?" Quelques paroles pareilles suffirent d'sxtraire d'einbarras tout le monde: le salud-sans-nom, le redacteur stupid, moi, Laurant Schwartz (chi m'avait fait le compliment: RpEx "Parfait!" apres ma con- ference, et aussi luimeme. C8est Mleyer che ne sait faire ca ---non e un.complimento. (') Meme apres notre article sur le temps locale de Paul Levy [Seminar 1990], c'est clair che Meyer ne L'a comprise ni Dellacherie. Tous les deux peuvent le lirge (gg humilite je conseil) deux ou trois fois en recourant a mon article pour des enseugnemnt che leur manquent e che leur profiter mathematiquement. Soyez didge d'un ecoliers dit "savant" jadis. STANFORD UNIVERSITY STANFORD, CALIFORNIA 94305-21z5 DEPARTMENT OF MATHEMATICS (415) 725-6284 9/9/1993 Dear Art, Congratulations on the deanship -- or is it provodtship as I heard? As an administrative head of a large urban university close to the center of political powers you may be interested in the following suggestions pro- vided you are in essential agreement with the idea. It is my hope that you will play an active part in its and not brush if off as being too busy to engage yourself. A front page article in the NYT to-day prompted me to write this letters although I had thought about it for years. An inspira- tion made me think of you as a possible starter. We all agree now that Americans are terrible at math, and that we must strengthen our math education in the schools. Why are our kids so weak in math? and how can we make them learn more? Of course we have too few good teachers, and our standards are too low. But then we say the kids do not learn math because it is hard* dull and without motivation ("useless"). So we must try to relate it to their real life, which in America sorry ) means to their jobs and making money. So we say that algebra must be taught in dollars and cents, interest rates in mortgage and annuity, maybe stock prices and futures; and geometry (which many high school students do not take) must be taught in building a garage or subdividing an acreage .... I stop here because it is getting so silly and so unrealistic as you and I know. In real life we do not need any math to do any of these things. Also* are such real- life illustrations really more interesting than (a+b) = ...? So let me just get to the point. (1) Elementray math should be taught in the traditional ways surely with examples (see above) and work-outs, and hopefully by good teachers such as you and me, but as just plain old math* not a manual to carpentry or in- vesting or even shopping, nor games [apology to Bertrand Russell!] kids play at, .... For instance* the multiplication table must be memorized, and the square of a+b must be either memorized or multiplied outs .... Students must learn such things without freedom of choice. Questions like "Why should I memorize this?" and "Do I need to know this?" ARE NOT ALLOWED. Yes* authori- tarian if not totalitarian. That is the only way to teach the kids math* and it was the way the advanced Eurdpean nations had adopted for centuries* and it is the way the Chinese* Japanese and Singaporeans use now. They have not done badly financially have they? (2) Once we decide on MUST-DO* the good old America CAN-DO spirit will follow. If the peoples mentioned above could or can do, why can't we? My answer here is (and that is my main point), we ask too many stupid questions. In this I agree with Bennett (whom Osserman e. g. called a reactionary): a college student should read the classics, no question asked. Admittedly . math is harder than the classics, the more so we must make the kids learn it wB eB B L- m not talking about W pseudo-Hunt process r I am talk- ing about he multiplication table and the square of a+b] (3) Yes for jobs and profitsK they must also learn computers and such. That is ANOTHER QUESTION. Math is Math and must be taught and learned as math. Yes there are some Wlw connections between computer skill and (say) algebra study, but that is a side issue. Yes computer skill may be requir- ed in their future employment [not many will be as lucky as I or maybe you] but do not confuse that with learning math as a separate and divisible MUST- DO. In simpler words: learn math on top of computer 101. to 0VTAK WH . STANFORD UNIVERSITY STANFORD, CALIFORNIA 943o5-zi25 DEPARTMENT OF MATHEMATICS (415) 725-6284 I can go on much longer but you have got the gist. Do you agree or disagree, Forget about "some reservations" for now. As I hinted above, in my opinion why we have failed is precisely because we asked too many questions and made too many reservations (for instance about disadvantaged kids in thatWpW of Baltimore). We have lost our famout CAN-DO by agoniz- ing too much over WHAT-FOR. Let us now just DO-IT (we can), and then ask questions maybe. If you agrees here is the next step. Let us organize a select (small) group and start political action. I do not know how the School of Educa- tion folks feel but they will have to engage. Media support may be neces- sary (have you seen some of the "good teacher" stories in the media?) As provost/dean there is a lot of ropes you can pull. I wonder how many of our math friends will support this idea or justhInterested in such an un- dertaking. If you will put your heavy down I am willing to write a few more letters* but maybe you can draft better ones. I am not a good poli- tician; I think you are. Judy can play a big role in this, and the local pols you know can take parts after all they have kids and grandkids too& and they don't want to lose out to those foreigners. Did you know that in the last international competitions the scores of the Americans and those of the Chinese form disjoint sets? Now I begin to wonder if my inspiration will work? Let me hear from you fairly soon if possible. Best regards to your wife and kids (whom I remember well when they all came). Yours Cordiallys P. S. Have I tol 'hiA*in one of my last cla es here, 44s two out of 65 knew the formula 1+2+...+n. One was fro Hongkong who said he learned it in high school (the sum was done in the 44 textbook taught in 41-43); the other bright boy just guessed it (bwa o American spirit) but he did not turn in the final and quit the course ---this was very American too. I told the then chairman boes he barely listenedlme out but advised me not to make it public. At the same time your Alma Mater was touted as number-one undergraduate school in the U. S.oin the Campus Report and in the Daily. But here I am not talking about that Gauss sum (at age five) but, repeat, the multiplication table and the square of a+b. Notabene. October 3. 1993 Dear Roderick: It was a most pleasant surprise your call last evening --- I was just viewing "Einstein" on PBS --- did you know that he had a ( bastard Liserl with A Milevas abandoned when they went to PTf be- cause at that time to take the baby there would cause dismissal? I knew from P61ya that E. divorced and married "a less attractive woman" [Polya's description] but did notabout his earlier ecandal.4 I write this for my own amusements and also as a TEST to see whether T-H has the capacity and responsibility of delivering this to you --- the probability is far less than 1, I estimate. In China often one hand does not know the existence of the other- Anyway I'll find out eventually. In 1936-7 I was in the King (or 4th) 0, A Dormitory (50P-) across the walkway to the BigMySa..Halls where otiej M one could have a complete supper for 8 cents. I used to pay /' 12 or 16 cents to eat a frshy-c oked dish, but some of my dorm-mates were too poor o too stingy to spend that much. There were also two smaller privately-run real restaurants in another part of the campus, where the adm'4rs (like youl) o lived i4a higher style. Once a senior student (who later 9 -' roomed with me in Kunming as grads) took me to one of these: .rr., even the po k Jiah was much tastiers cost (I think) 16 cents. - Nothing of this kind remained when Kiang Tse-han "Z:- -, (p) took me there in 1979, when I "led" (chinese expression) tk ) Doobs and Neveus for an official visit! ... I don't think W I kn9o a single mathin there now, because at one time there V were f engineers. If you find anyone worthwhile let me know. T-H boasted of its Physics# but three of us: Ygn (who went to e Paris)s Wang (dead, Chern's protege) and I left Phys. for Math. Why? Because we found the teachers NO GOOD --- some are still living and become bigshots, Chinese manner. Just in case you would enjoy doing its you W try to / find a -(prof. of civil eng.. better known as son-in- . law of a previous press. Wi- f ), Call him in and tell him I want to know if he ever delivered those photos to my friends 4a. uaehnu? He was our garde ner for many months and is / EXECUTIVE OFFICE OF THE PRESIDENT OFFICE OF MANAGEMENT AND BUDGET WASHINGTON, D.C. 20503 April 7, 1994 Kai Lai Chung 903 Lathrop Drive Stanford, CA. 94305-1059 Dear Ms. Chung: Thank you for your February 6 letter to Leon Panetta, as well as your letter last summer, regarding his usage of the phrase "with regards to." We at OMB tend to focus more on the substance than the style of the Director's comments. However, there is always room for improvement, and we appreciate your comments. Sincerely, Barry Toiv Associate Director for Public Affairs 2 W-euj 4-Z k 659-U 0,-,- or -q ) 9V~A7J?1/L" (c&-'L 1)h 41-gAL Cte VQ.a4 liierzv C *C1 u-4 LvcQu I. (e(6n Jl Cae/sek ,2e ^flI4 iin" -- '/5 - v /, )' A fl) I- kC/y L4e41; I+1-7, cr 1 31 4; 6a4t, 6l/0 AC kz^ Y""I5 v'LJt-PzLJ 3 UP CC vJ'L /A NS s rl-a " k'" O-cy-^I Rc)R~ ~ ) 'CL1, rv-;)y&W d414141 el~---t 4t L u--,V e c (/. Cc/, *I ^lLs^ ^^Sfi^ -rrc4 eof CA44-4~^ a MP -4 / M ~a~e~e~ ete /C;a~ ; r CuaJ/ Date: Thu, 28 Jul 1994 08:05:45 -0400 (EDT) From: "Rick Durrett" To: ebdl@cornell.edu,sek@math.cornell.edu Cc: BCc: Subject: from K.L. Chung X-NUPop-Charset: IBM 8-Bit \def\u{\underline} Professor Kuznetsov (and Dynkin): I would like to know whether you can apply reversing to my problem for 1-dim Brownian motion. Pierre van Moerbeke posed the problem as one of time-reversibility in Schr\"odinger's quantum theory (see Schr\"odinger's paper c. 1924). When I started the {\u natural} time-reversing with Walsh in 1969, I had hoped that this would yield useful results for a "reversed process" (cf. the "dual process" constructed by other authors, which do {\u not) have to do with time reversing), so that the major results in classic potential theory (see Hunt's third paper (in Russian) and Blumenthal and Getoor's book; or the last chapter of my Lectures from MP to BM) can be proved by reversing as it should be (comme il faut). But 25 years later, this has yet to be done! Otherwise, why reverse? Yours truly, Kai Lai Chung Bad news: I saw in the AMS directory that Lennart has moved to Stockholm but please try to deliver my notein person, In your e-mail you said Mit- tag-Leffler in Stockholm --- ain't so. arch 2, 1995 Dear Dr. Zambrini: Thank you very much for your letter explaining Al's careless writing. I do appreciate your willingness and promptness. I also know that the silly tau Al had there was for a purpose that he needed in his derivation (of course I gave a better one even with the same random walk type of discrete approximation). But I had long since figured out what he meant there, in our notations NOTHING but 1, n ^ e\ -M EB(t) ] = dt / er Thus (and this is very important for the question on hand]: ANY t will do! The sling above is exactly what he needed therefore his heuristic doing* and tur ed out to be also what is needed in the Ito integration. Did you know Serge Bernstein ]I bet he met with A1.] already had his random integra tion exactly like the above. Having said all this* I am afraid your expla- nation is too long for inclusion in my brie- historical perspective, where I nad copied down that paragraph in Furth's translation that I sent you/ I will say that I discussed this with you (also with Prank Knight who in his book apparently totally misguidedly followtdg Al without realizing the faux pas --- I wrote him too but unlike you he has not yet answered), .... If yok can send me a short one paragraph (less than one hundred words) I may yet copy it instead of Pust mentioning it. I have another favor to ask you. Please give the inclosure to Lennart* and insist on getting a reply from him on the spot* and repeat it to me (as you do very promptly). I am most annoyed at his mealy-mouthed lack of res- ponse. He is a bit spoiled and must theifore be coerced into action. Please fax or e your reply inclu Lennart's as soon as possible. Thanks a lot. [By the way I plan to be in Italy in May and can fly to Lisbon for a few days proved you pay theULirfare---far too much in Europe. But don't do it unless you want to!'] Q i P. S. Please hand over my note personalt~n~r eson and wait for his answer. Don't trust him if he says he will reply. INl t OLAv March 2 1995 Lennart Carleson Kai Lai Chung re old letter Many years ago after I saw you here I wrote to ask you to confirm or deny that you had said Emile Borel was your "hero". Maurice Heins told me that even longer ago. Please say a few words about this hearsay. I am asking Zambrini to get an answer from you --- too long delayed but still interesting to me. "'ith Kind Regards, 61 q/buLf i^ U^- w , I/^ '< STANFORD UNIVERSITY STANFORD, CALIFORNIA 94305 DEPARTMENT OF MATHEMATICS April 9-11. 1995 Chen. C. Q. A A1 IA -Inel d- a copy ef my old paper with Rae. I do not knew if anything good will eeome out of its all I knew tos that NOBODY has serious ly tried. It is curious [math. is largely a question of curiosity] that I can get Gauss's minimum energy so easily from the last exit tumea dis- tributieo. Your teacher Silverstein was just writing his symmetric MP papers when I told him my method (in Princeton). He said it was a new idea but so far as I know he did not pursue it. It takes a younger and mere vigorous person to try something new --- most math'ns only stew in tfeir own juices because it is much easier and gets faster results. My other suggestion is to start with a new hypothesis for the class of q: lim sup t.p lql(x)ds = 0 t4O x 0 h s to de the conditional gauge theorem and its consequences. Without the h (any harmonic fucntion, but specifically the Lip kernel K(.z) and the Green function G(.y)) the hyp is that of Aizenman*Simon which we used in our book. I found that this new hyp. is almost the same as the old ones so that the class J of q is almost the same. Then I told Zhas to try to prove the results about conditional gauge by means of this hyp., directly, just s I did with the gauge theorem etc.. He is too lazy and tee ignotan1 to try it. Of course we do not know if the method will work. But one eust try first. Please tell me at least whether the energy relations in the inclosed paper can apply to the Dirichlet forms? Historically they came from the same source. It seems to me that you have not heard about this before: the French school of potential theorists: H. Cartan. Chequets Brelets Deny, .... [even a litter Malliavan]. You should read Beurling-Deny's "famous" paper to see what these people were doing ]without probability]. Pukushima learned something from them. In order to be a one should hot be content with being a The majority of American Ph. D. students never learned anything when they were doing their thesis. But the better ones begin to expand their hori- son after they begin their career. That is where the dividing line be- gins to show. COPY Jan. 31, 1996 iear Heinz: I have deliberately called you in the American and contemporary German way. I must also beg your pardon to say that "the loss is yours" regarding your delayed (but full) response to my litt'1 didactic question. Had I got an answer by Mlay* 1995 you would have figured also in my Green. Brown* (sic for ,) And Probability. If you have the time arid curiosity. please read the passage where this is discussed. One thing you brought out very clearly (I only saw it vaguely) that the symmetry of Green's func- tion is essential in the point-of-view you told me. So here is another IMI'ORTANT question which this time you may wish to answer quickly so that your answer will be used if and when the occasion arises. ','as that symmetry observed first by experimental physicians before Green "discovered" it mathematically, see Note 17 in loc. cit. It was k1wn as reciprocity in electricity and discussed by maxwell. Is it easily tested instrumentally? l.ote we need to check all (or approx. all) positions of (xsy) --- not4yto do even with the then-uninvented machines. I trust A that a learned German scholar would know the answer to this (I think very interesting) questions but my American colleagues know nothing. A lesser but still interesting question, in case you knew Green's C 1828 Essays (it must exist in German), is why Green was unable to prove (of course under unspoken smoothness conditions "topology" was not known at his time and physicists certainly did not care for such finesse) the symmetry by using his own formula(s) as I did in my book. [Of course rigo- rous proofs wrye given e. g. by Kelloggs probably 4 by such as gzkoitz ixam Sternber n the Sammilung Ggschen. I am speaking of a physicits' "proof".]J It is a pity I did not see you in Hong Kong, but if you come nearby please let me know. With kind regards* /?/Feb. 1, 1996 Dear heinz: It is a pity that we missed each other by a day or two in H. K. Unlike you (although that was not your habitual behavior; it would have been habi- tual for a Frenchmans not a German like you) I answer my mail immediately* unless I do not want to. "The loss i' yours", as we say. If you had behaved in your normal way you would have received a NOTE after my remark on p. 5' of loc. cit. [rather, the book announced in the inclosed green sheet]. I just wanted to be sure that the result was known for other [I should have said Marcel Riesz] poten- tials. In that case I could [and ww&'] add another note on Marcel too. At the time I wrote yous I was foolish enough to indicate a proof of (8.11) [in your letter, it is (1)] by using the uniqueness theorem i. e. Prop. 3, p. 186 of my Lectures (1982), instead of the more apyprpriate Prop. 6 on the same page. [How careful I was in writing these two by side, but 13/4 years ago.] Now you correctly pointed out that Prop. 6* the Represen- ta in theorem)is what I should have cited. So I did OK in my book (loc. cit.A). But one more things after I read what you sadd about PWI resoluti- vity (whidh is a litteV "beyond" me) I suddenly rei ized that there is also UNI(QUENESS for \'iener's genralized solution of the DBVP, indeed I wrote it down explicitly in Prop. 11, p. 186 of Lectures. Thus regularity is not needed there either; but please note that thd argument is deeply stochastic 10:) [Doob's .doing]. Als o alleges iJt in guter ordnmng. ninht w-ahr mein Herr? Now I have two more questionsAwhich you may know the answers, or maybe you will be kind enough to find out for me from your earned German collea- gues (the likes of Sternberg?). which my American col agues neither know nor care to know! (1) The symmetry ofGreen's function is k&own as electrical reciprocity discussed in Miaxwell's "reatise. That electrical phenomenon was known before Green discovered it c. 1828, see Note (17), loc. cit. Was it experimental- ly observe f'.st by physicists? by whom? Let us stress that it cannot be so easy be 3f theoretically we'must test all positions (xy) for a conduc- tor of extremely odd shape. Even modern computers could hardly do that but of course physicists are not so exigent and would be satisfied after say 100 trials. Still it would be most interesting to know if the fact was observ- ed before math was 'done??? (2) As I said in Note (17), Green showed surprise at his discovery but had to ask PROF. Maxwell for a "proof". I could not understand the latter given in the Treatise, so tried it myself found it q ite easy from Green's old formula. Of course rigOrous proof (was given e. g. in Kellogg's book but I wonder why Green could not do it (without worrying about smoothness etc. of course* that was standard in 1828) Now how do you prove the symmetry in your axiomatics? Best regards, / 6 " N. 1. It is not only American but tery German to use first names now, (+C:., Feb. 16. 1996 Dear Lindval: Since you are the expert on coupling please give me a precise reference as to: who was the first and which was the first paper or book in which the coupling method was used to prove the COMPLETE limit theorem for the transition probabilities p(n) of a denumerable Markov chain? Doeblin or Kolmogorov was credited to have the idea around 1936 of coupling (for D. only in the finite-state case) but that did not mean either one of them used the idea to prove the following: For any ) and js there is an integre d=d(ij) such that m(nd) lim p exists >0. n ij I saw such a proof in the MS of Kallenberg, but when I asked him about a references he gave me Kolmogorov 1936. That was foolish because I knew perfectly well that Kolmogorov proved the above theorem in his 1938 paper (in Russian, with a previous abstract) by a TOTALLY DIPPERENT method. [I'h not sure you know that proof?] and I am not sure if in that paper he even mentioned another proof by the coupling idea. I have not seen your book on coupling [sorry I won't check it but maybe you will be kind enoughX to tell me the correct history? Please send e-mail as follows: chungamath stanford.edu as soon as possible. Sincerely& P. S. Perhaps it is necessary (in view of folks like Olav) to beat the dead horse a little: once the idea of coupling is given it is easy of course to prove the limit theorem above in (say) a positive-recurrent class, or some such special situation. It is my opinion that it is not quite "trivial" to use the idea to prove the COMPLETE theorem stated above, L q e, J4f "rs t rti -, [which, I repeats was give in Kolmogorol's 1938 paper for the first timp Another nicer proof but without coupling is given e. g. in my Markov chain book, depending essentially on the theorem by Erdc4-Feller-Pollard that can be stated without any intimation of probability or Markov chain. I assume you know the latter well (see Feller's Vol. 1. not 2:) By the way it may interest you to know that according to Yushkevich the latter proof WAS NOT KNOWN IN Russiasha-ha. -y eltl\ c-A 5X 'At AfIf @rc-t mt (&1ER V I, March 135 1996 Dear Torgny: Thank you for your rep&y which arrived a couple of days ago. I cannot use the computer so must write you but you can out the time for communica- tion in half by reply this time by e-mail : chungamnathstanford.edu The probability that one of the secretaries will print out your e-mail and give it to me is quite a bit less than one but let us try at least. I do not know what your definition of "null recurrent" is. Please spell it out. By and Feller's definition is that for all i we have p(n) .0) plus recurrence we shall assume that we are in one "class"). Obviously that is not your defition because on pp. 9-40 you wanted to prove (9.1)* which follows at once from my def. Now let's see what you did. You assume (9.2) to hold [I don't know Oreyls proof, then you suppose (9.1) to be false and obtain by a cute diagonal argument [Is that yours? ] a stationary distribution. Fine. Then you said "But there is no such ... if X is not positive recurrent". I don't follow your logic because I do not know your definition of positive/null recurrent. Please explain to me what you mean. Of course I can finish it off my way: since you are assuming (9.2) (to me that is a "big deal": are you sure it holds in all trans aig apd recurrent cases by Orey's' proof? Of course I know it.is true romjresults 4Qg incorporated in my Markov Chain books which CItha*.of Kolmogorov (and Feller). long before Orey ---I am not quibbling abiut credits for dead persons but I am interested in your logio!] ... Repeat: .Af (9.2) is true in the null-recurrent case you are discussing then it *S09 follow at once that t p(n) .> x in your notation periodicic, Since you showed at leaU one i >0 that is the contraohtion you are seeking. SSo what is your definition of "null recurrent"? There are some misprints (?) on p. 40, on line 9. 1 should be j; then on line 11 you should say "for all i". Finally, may I nitpick your use of the word on line 18: "Actually". I bet you mean the Swedish 'avitz" [I don't khow the spelling but Jean the word all the time in Swedeni it is the same as the German Jawohl.'J but it does not work in English. You have reached your goal and should have simply said "Thus (also in German 3 (9.1) is true." Those elegant words "are now set" are fit for poetry but not so clear logically. "Set" means "laid down", "put there" in English: it does not connote the end of a proof. Now I like the poetry you cited on 234, Qan 'YON jh 01 ;t Of course the first is better than the second* but if Robin is a living person please tellftM fixme that I suggest a major improvement of his translation: "farthest" for his "furthest" --- that is clear. When I get your reply (by e-mail?) I will propose a very cute pro- blem for coupling. By the way when I wrote you last time I wanted to know whether that diagonal argument to ger -m had been introduced by (1) Doblin [the way he wanted his nAge to be spelled!] (2) Orey (3) Lindvall (4) None of the above: who? Best wishes, do take my comments with a good Viking sense of "fun". Sincerely, P. S. When is your next visit here? March 29, 1996 Dear Torgny: Yours of 3/21 with OreyLs pages arrived. Thanks for being a prompt correspondent. Let me say at the outset that my queries aYe not about the "truth" of the final results (which were Kol*s anyway) but about your [and poor Stevels] presentation of *4. Steve's was somewhat clearer than yours but it was also unnecessarily tortured [a poetic adjective]. Your former colleague Olav has a much clearer presentation in his new md., whlih was my original motive for writing you. To be franks as Swedes are reputed to be, you DID NOT ANSWER the ques- tion raised in my 3/13 letter. Read it again! How did you contradict null recurrence from the existence of a stat. distr. ? You gave no argument. Steve's paper did give a contradictions using his main theorems but in your treatment you singled out the null-reacurent case and thereby further confused the issues. You will have to ask 0Ov to send you his version to learn how much simpler all really is. Steve was a former undergrad stu- +#K%; dent of mine (in Cornells 1949). He wrote very badly (as Jainkabout ano- 0t1 their of his paper that Jain straightenteoed out, contained in Jain's Ph. D. thesis) but that can be excused because he was "young" and excited about ha nhis "discovery". A book author does notkthese excuses. Now let me tell you an easier approach. This does not neid Steve's theorem (once the main limit theroem is proved as in my books that theorem is an easy corollary]. It begins with the elementary besaro-mean limit theorems p. 33 of my MC akatz book (2nd ed.) Corollary; for a direct proof see p. 56. Then if we use ygur definition of null-recu rent i. e. mi =0o for all i. we have (1/n41 (P) converges to 1/mii = '0 ow if(i) is a stationary distribution (as obtained by Steve) then you can prove at once ni is equal to the Cesaro mean limits hence 0 in the null case accord- ing to the definition you adopted [NOT KOL's or Peller's]. That leads to the conclusion desired, WITHOUT 4Mk the tortured contraposition. Think it through please and present it this way in your next class, just for a varia- tion of your routine. While the Cesaro mean limit theorem can be proved by simple analy- sis, some authors may not want to do it as a preliminary. Then I must say .you still have not explained to me why the existence of a stationary distribution contradicts your definition of rnTml r0umrranc That is the central question I asked you in my 3/13 letters to which please now reply (by e-mail?) Olav has rearranged Stevets thoughts in a more economic ways but you will have to ask him. In my last letter I promised a cute problem of coupling. If you are interested will send its but only after you explain what you mean on p. 40 of the pages you sent me. I am curious to know your arguments alth- ough now I have figured out TWO different ways to skin your catr-- sorry for the cruel images must stop. (4A , Nov. 12, 1996 2 N ) \V Al Dr. Liao: Thank you for sending me your solution. It is similar to mines so I am now sure there is no quick way. For the necessity of (2) for (1)9 one can take a shortcut: Suppose 1 = En u n = En all ni O Then &-nul = n3(u -ul), where we may take ul to be the minimum of all u Hence if for some m>l9 we can take n=md where d is the g. c. d. in (1) we get d = 1. Here is another little exercise (that I am going to mention in a talk for celebration). If X(t) is the BM in R we know IX(t/ is a .positive supermattingales hence it has a finite liAit a. s. as t-a)o. This was first shown in Doob's paper (1954), and then he said "the limit is obviously 0' Not that obvious! If you have a chance to teach such stuff try it on your graduate students. Of course a good enough one can probably prove it by using the transition probability etc etc. But after a while a quick prdof occurred to me which can easily be ex- tended to more general process X, assuming the supermartingale. In Chinese we says i 4 Maybe you can try it and let me see, If you have a sabbatical you may consider coming here for a quarter or soi as a Ph. D. here you can request some teaching assAgnment (with pay). Although there is not mudh probability left here there are other fields... Johnstone (remember?) is the chair of statistics and can give you a jobs I hope. You have to ask. I~LC/YYIID1~ /CI~ ~ccuRt ' fW i 0 Dec. 18, 1996 Dear Professor Halberstam: Thank you very much for your letter and reprint. It was a pleasure to have talked with you. Your article on Hua brought me back almost eje4f 60 years. I was a student in his classes* assist- ant and "would-be" M. A. [that's all Hardy got] candidate, but I went off and finished my j. A. thesis in combinatorics. My recollection of HuaLis ambivalent. You have chosen very accurate adjectives and adverbs in describing his prodigious talents. But he was not a genius in the sense ErddA was, and the majority of his work(s) must be called technical inspitieoccasional brilliance. Hardy gave Littlewood only 40 = Hilbert's 80 (1/2), Mordell 5 [is that correct?). I wonder what he would have given Hua? So far as I recall there is no published mention of Huae.by either Hardy or Littlewood --- correct? I recall very well my once asking Hueahow Hardy would have graded Titohmarshe whose book educated many Chinese around 1938. This kind of rating is of course ridiculous (in the New York Times, the media person asked Graham if Erd6s rated the top ten --- how far can we fall?), but for Hu& it counted. Everything he did then (c. 1940) he claimed as a "record" such as his correcting and lowering Vinogradov's circle pro- blem exponent. Until I read your articles I had not realized that he had given V's estimates their good formulations. Russians are noto- riously sloppy. I also recall Hue's showing me* on a pad on his laps before I partook Mrs Hus's red-cooked delicious pork (we were in a starving diet then owing to the Jap bombing), the twice 2n-raising 'd h^ of powers in a trigonomet3ro sum (7) of Mordell's.f That impressed me. 4v b met Mordeldyears later in Stanford, with Van der Oorput.] I don't think HuL gave good mathematical lectures when he came back to U. 8., certainly not the one he gave here on several complex variables. Could he "compete" with Carl Ludwig Siegels whose transcen dental numberdsI still have classroom notes. I enclose also a reprint about Hua's "mathematical economy" work you mentioned I did not hear ee k4t talk but Eugene // (-9 Sidney) did in Chicago. I am a little ou- rious if anyone there caught on to him? Of Chen I know next to thing, and am pleased to learn that he had human traits and would have wanted to remain abroad --- I've not heard this. He deserved our sympathy. Must stp here but should be glad to have further exoha es at your pleasure. Sincerely Happy New Yearl i 3 _9, tix4 4 P December 351 1996 Dear Professor Bolthausen: Inclosed please find the MS of "Probability And Doob". It was typed by myself and repeatedly amended. Please excuse the im- perfections. If there are errors or needed explanations please e-mail me and I shall reply promptly. Can you say when it$n 'appear?
Let me explain one remark in the Foreword: in the U. S. certain
editors insist on certain "conventions" which I have not followed
here. For instance they would insert an "and" between ")1WX/ Feller
and Doob in "Hunts Feller, Doob". You and I know how silly that is.
In my recent book I have to insist that there is a comma between
~fixr xa "Bron" and "And Probability". You will regard such matters
as trivial. The lack of a formal Bibligraphy or Refrences is a more

serious matters but I decided to be informal about it because anyone
who really wants to find out should be able to do so with the brief
indications (year of paper, etc.) given by me. As you must know, to
compile a list of papers is not an easy affair; most authors just

does not have ",'ur ..." in the title (at least in the Selecta I have),
so even Levy copied it wrong* but not Fr6chet.
Kolmogoroff was spelled so in its first appearance because that
was the way printed on his Ergebnisse! I refuse t1& spell Khintichine
Once more, many thanks. Do let me know if you have any "problems",

P.S. I was unable to track down the origin of my Footnote (1).
Please fill in with correct German "es convergie" or "sie ... ???"
unless you know the original form. I asked Klaus Peters.

F1ee/ July 1 1996
Dear Hans,
I forget which univ. you are at, hut trust this will reach you and
(1) Have you heard or seen the book advertisedd" in the Green inolqsure
If not* please write a FORMAL [TYPED] letter on your stationery paper
to say so. The stupid publsiher simply did not know how to sel!. You
should be interested and perhaps even shocked by some of the things I said
there: A Volume 2 might well include stories about you....!
(2) I am sure you know Aebi and Zambrini. The latter wrote me an 8-
page letter complaining bitterly that your pal Nagasawa and Aebi STOLE
from his early work on Schr&Ainger's ideas (In "Euclidean Quantum ...."
which you must know about). He also sent me a copy of Aebi's article in
him
the Math. Intel. and called/a "baby crook", since N. is the senior crook.
He said the two literally "copied from" his prior works) without even
mentioning him. Is that possible? YOU are also apparently somewhat in-
volved [recall you did somethig- bout Sohrodinger.too. no']? though you
wevw not accused. Please tell t, /Wha4's all this, and try to giveyZ. some
oons de nation. I know disputes abo 4or4ity are common v usually among
weakings such as statisticians, but Zambrini whom I met seems to be serious
enough. Let me knw what you know and think, but please do not tell your
pals because frankly it is none of my business.
(3) Here is aldrue sto ryabout the organizezwof the ecom. conf. you
came to. He audited ny elementary 'd&es where I discussed Markov chains.
I wrote Ep (n) = 1 lim p(n) = x

j ij n ij3
The famous STEADY STATE -- the ONLY probability 95 per cent of such f&&ks
know and TALK about until recently a number of "other crooks" like Thom
coined CHAOS I Then I asked the class .:dsn't it f*o then that
ntE = 1.
YOU must say it in a SINCERE ways not rhetorically. I think I succeeded.
That prof. of math ecom. said: of course. You want to know hisja? ?
To his credit he did attend the next class when I had Elton Xu ghd"you
must know by now) to go to the board and show ... The trouble is au gave
a bad ex. .. you think this would not happen in your seminar in Berlin
or Bonn* FIND OUT BY simulating what I did in my class."" |
D16y LA 4-,_7 212 2//1^4^

fllmer@SABSNS.sns., 66:20 PM 3/11/97 letter

Date: Tue, 11 Mar 1997 18:20:20 EST
From: follmer@SABSNS.sns.it
To: chung@gauss.Stanford.EDU
Subject: letter

Dear Kai Lai,

yes, I did receive that letter and I feel quite awful
that I have not answered so far.
The reason (not a good one, but just to explain)
is that I did not know immediately how to answer (2),
so I wanted to check first what the problem really is,
and then I somehow did not get around to do it.

I am giving a series of lectures at the Scuola Normale
in Pisa. I enjoy this a lot, except that I am not
familiar with the local e-mail editor and do not
succeed in correcting preceding lines. So don't be
surprised if this letter will be somewhat messy.
A
As to (2):

This is a very unpleasant feud, and in my view utterly
superfluous. Nagasawa and Zambrini have both worked on the
duality equation for diffusions which extends the classical
Kolmogorov formula for the density of the invariant measure
from the reversible case to a general duality setting where
one relates the forward description to the backward description
(time reversal). The emphasis has been different, but both
are motivated by the application to quantum mechanics and
to euclidean field theory. This was emphasized by Nelson in
the sixties and seventies, and Zambrini has been in contact
with him. But it appears already in the work of Schroedinger.

In my view, the work of Zambrini is o.k. somewhat
formalistic and not very deep, but serious. Nagasawa
has worked on the duality already much earlier, and then
has come back to it, with special emphasis on the interpretation
in terms of quantum mechanics, in the eighties. He has had ideas
which I find more original than in the case of Zambrini,
(and which have been made precise in joint work with Tanaka).
Insofar they are related to large deviations theory, I do not
always think that Nagasawa (or Aebi) treat this aspect in the
best possible way, but it's certainly o.k.

Of course there is an overlap since they both talk (and write)
about the same basic structure. But in my view it is silly to say
that Nagasawa/Aebi "stole" from Zambrini. The key part of
Nagasawa's contribution (construction of an underlying particle
system, with Tanaka) appears nowhere in Zambrini's work.
Nor does the connection to large deviations which is emphasized by

Printed for Nurlya Janss 1

fllmereSABSNS.sns., 06:20 PM 3/11/97 letter

Aebi. The basic duality equations, and various easy variations
on that topic, appear on both sides but they were known long before
anyway (and certainly earlier to Nagasawa than to Zambrini).

The problem seems to be somewhat psychological. Nagasawa has been
directly to) Zambrini, and has not given him much credit (not even
giving references to his work). Zambrini has reacted very strongly
and has apparently written very nasty letters to people in Zuerich
(even to the dean of the faculty if I am not mistaken).

I have remained on speaking terms with both and want to keep
it that way. It is just a somewhat childish conflict, and
Nagaswa is probably the one who started it by being aggressive in
a way which was in no way necessary.

So much about (2). I am sitting here in Pisa and so I have to a
little vague: all the papers concerned are in Berlin, and I have
not looked at them for a long time.

As to (1):

Yes, I have somewhere seen an ad for "Green", and I have ordered it
but not yet read it carefully. At first sight I liked it a lot
(like Lang, I feel that there is a strong need for such texts
which make the effort to provide some historical perspective).
I look forward to reading it more theoroughly as soon as my next
course in stochastic analysis comes up.
I was not shocked even though I simply cannot say such things

As to (3), I have some guess. And I may actually do that test
in my introductory probability class next term.

Now I send this off (but I am not yet sure that I can retrieve
a copy to send you by air, since the local system here is beyond me)

with my best wishes! Hans

Printed for Nurlya Janss 2

Wolfgang Stummer, 01:20 PH 4/25/97 Re:

Date: Fri, 25 Apr 1997 13:20:00 +0200
From: ws@mathematik.uni-ulm.de (Wolfgang Stummer)
To: nuri@gauss.Stanford.EDU
Subject: Re:
X-Sun-Charset: US-ASCII

Dear Ms. Janss,

thank you for your help with Prof. Chung's email. Here is the
real message I wanted to send him.

Wolfgang Stummer

DEAR PROFESSOR CHUNG,

THANK YOU VERY MUCH FOR YOUR LETTER.

IT WILL BE A GREAT PLEASURE FOR ME TO VISIT YOU IN ITALY IN
JUNE.

SINCE OVER HERE THEY GAVE ME SOME EXTRA LECTURING TO DO WITHOUT
TOO MUCH TIME FOR PREPARATION, I SHALL BE ABLE TO COME FOR JUST
A LONGER WEEKEND (THURSDAY TO SUNDAY, INCLUDING THE JOURNEY).

I WOULD PREFER TO COME BY TRAIN BUT PERHAPS WE COULD RENT A
CAR AT OUR MEETING POINT. IN PRINCIPLE BOTH
PISA AND MILAN ARE FINE WITH ME. DEPENDING ON
YOUR PLANS I WOULD MAYBE HAVE TO FIX AN ACCOMMODATION IN ADVANCE.

ALL THE WELTENDS IN JUNE WOULD BE ALRIGHT EXCEPT THE ONE INCLUDING
JUNE 14 iD 15. ,

WOLFGANG SUMMER

do

Printed for Nuriya Janss 1

4/27/'97
Dear Stummer:
I got your email from Nuriya Janss (Mrs.). I sent you an email
via Corinna. Both ean send email for me and receive yours. It may
be faster via Corinna as I see her everyday, but not Nuriya.
It would be a [/easere to meet you-again-after almost 9 years, and
to make an Italianesche Reise zusammen. It may be just as well to
go by train if you prefer; but as I said I would be glad to rent a car
if you are ready to drive. In the latter case we may have to fix the
rental in advance (using one of the big rental agencies such as Hertz,
Avis, ...whiah are reliable and have fixed relatively economical [your
field of expertise] prices and easy to return the car etc./f Maybe you
know a German agency that will works but if we try to rent on the spot
in Italy there may be problems! They "cheat" tourists1 certainly in
France when U did, long ago.]
The most important datum is the date of our start. The long week-
end from June 20 (Friday) to 22 seems optimum* so that you can take
a night train from Germany to Pisa or Firenze

we mathematik.uni*ulmode (Wolfgang Stummer)

Dear Stummer,
GlAd that we can meet again. The optimum dates are June 20 to 22
and we can meet around Pisa. I love the train but we must decide
where to go. Any suggestions? I will write you shortly. Please give
me your home telephone number and tell me what is the best time to
phone you. You can reply to the mail address in this message (faster)
or Nuriya Janse. Saluti. CHUNG

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(Jawngn. Su9j;ToA) ep*nmT un*T1UWeqWn SMA

Dear Stummer:
I am sending you an email of which this is the long version.
It would be nice if you could meet me in Italy and we travel
together for two to three days.
(1) the weekend of June 20-22 (incl.) Friday to Sunday is the
optimum satisfying your conditions and convenient for me.
(2) By that time I shall have finished with Scuola Normale Sup-
eriore and shall be at Lerici (ever heard of it?). We can meet
there which is near La Spezia a big train station. We can decide
on the meeting place later by phone if necessary. I can send email
w1en I am in Pisa but not in Lerici. Please give me your home and
office phones, and the optimum hours to phone you at either number.
(3) We must decide where to go. In my eaJier letter I said
I would like -o visit some beautiful cities to the east of Milan such
as Ferrara, Mantova, (I have been to others like Parma and Bologna).
But to do that it would be more convenient by auto and although the
distances are not much they are farther from Milan and Pisa. So
maybe it would be simpler to gb to the Italian riviera. Natures
not so much culture. La Spezia is extremely near Cinque Ter e and
we can take long walks there. You are a superb mountain cli r but
I cam only negotiate low slopes (as you remember on unser land!)
I have been there once, with a German from Bielefeld. In this case
we can rent hotel rooms maybe in a central spot. It should not be
too hard and not too expensive. I have the Michelin guide and there
is a German guide from which you can choose the location and hotel.
After that I would like t6'go to Santa Margherita (near Genova)
of Portofino (the latter is more "snob"). On Sunday night you may wi
wish to go back? I have hiel reservation in MilaA for June ai Z3-B
but prefer to stay elsewhere before then. aW=Vr^MW can go
to Como before you take the train via Switzerland (a beautiful route
that I have taken more than once). In that case I can stop over-
night at Como --- "kein Problem.
(3) Please make suggestions for a revised scenario! by e-mail.
Auf wiedersehen Best wishes, a /0o -

May 1, 1997

Dear Professor Da Prato:

This is to inform you of my plan to visit Pisa. I should like
to thank you once more for your kindness in allowing me to stay in
the Timpano (for a "second chance"). Zambrini asked me to give a
few lectures to his Grupo of mathematical physicists. So I am going
first to Lisboa (May 26/7) for a few days. On June 4 (Wednesday)
I shall fly by Alitalia via Roma to Pisa* with scheduled arrival
time %:20 PM at Pisa Airport. This is a little late but I hope it
will be possible to get into the room at Timpano. Dr. Domenico Accor
intis who was at your Scuola in 1989 (in classics, not mathematics)
and who knew yous has written to say that he can take me from the
airport to Timpano. In this case perhaps he can obtain the key to
the room before he meets me at the airport? Otherwise it may be
necessary to make another arrangement to let me into Timpano after
(possibly late) arrival. I am sorry to trouble you with such chores
and hope one of your secretaries can do it. Domenico's telephone
number is 050-5618635 he and his family live at Molina di Quosa.
It would be an honor and please to give a talk in your seminar&
more than one if you wish. May I propose the title:
Introduction of Random Time in Physics*
the same as in Zambrini's seminar but more advanced and condensed.
The material can be found in my booklet: Green, Brown* And Probabi-
lity. This is for a general audience without technical novitalv--
please tell me if it would be suitable. If an announcement is neces-
sary you can schedule it at any day and hour for your convenience.
It is my present plan to leave Pisa in the morning of June 16,
but if the room is already booked on June 15 there is no difficulty
for me to leave one day earlier. Allow me to pay the rent for the
duration June 1 to June 15.
Please send me a reply by e-mail as you did once. Can I have
also your telephone% and the hours most convenient for telephoning
A
you either from Stanford or from Lisboa later. Thank you very auch
and looking forward to seeing you again. Con devotissimi Salutil
Yours sincerely,

Email: chung a math,Stanfordg du

" Aec6 g/5y

1s M -

May 2, 1997
Mrs Joan Lally Lombardo
Localita' Romba' No. 7
Lerici (SP) 19032
Italy
Cara Signora e Caro Signore:
Mi e' piacouto parlarvi un po' sul telefono. Siete molto simpatici
tutte e due'/.
This is my "planning ahead". The old Orario I have says that there
is a train No. 3260 from Pisa to La Spezia, arriving 12:10 (mezzodi')
If it still runs, I will take it. Please meet me at the stazione. There
is also an 10 arriving at 12:34. If I miss the other one I can take
this but IC trains are ofien pieni S4lio non ho fretta.
Dicono che Signora e' buonissima cuoca. Can you give^lunch after
arrivals verso 1'una (1 PM = 13 ore)? A me pace la pasta casalingas
un po' di pesce se c'e', una insalatas due bicchieri di vino. E poi
jr prendergnpisolino.
If you are not too busys you can send me the train information
above. I leave for Europe on May 26* so quasi quasi c'e tempo per un
scambio di letter. You can also send the train information later to:
c/o 84Ra Liviana Pauletti
Dipartimento di matematicas Universita' di Pisa
v. Buonarroti, 2
156100 Pisa
I will phone you from Pisa before coming. Ciao e Saluti!

Fax: (415)725-4066 per K. L. Ohung
Cargo Domenico:
Thank you for you very nice letter. It pleases me ver much that
I will see you and your family again, soon, and we can enjoy a visit
to Volterra.
I have booked a flight by Alitalia from Lisboa via Roma to Pisa*
on June 4 (merbokA4i=Wednesday): arriving at Pisa aeroporto (se non in
ritardos attenzicnef) at the scheduled time 8:20 PM = 20:20. It is a
little late but hope you can meet me there? If so please telephone Da
Prato or Timpano to obtain the key to my room in the Timpano. This is
necessary becasue at that hour there may be nobody at the office in Tim-
pano. I have already written Da Prato and told him that he should get
the key and give it to you if you oan come. Since you know both him and
Timpano so well I am sure this is easy. Thank you for the trouble. I
may be able to telephone you from Lisboa on June 3 or 4 to remind yous
but that is not certain. Potrebbe 4onfacile L farlo appunto.
Congratulations for the publication of your virgin book! From phat
you told me (taking your class to Romas merav&gliosiv splendissimi!),
your position at the Liceo is a very honorable one. Of course you may
prefer to go to Napoli (nearer Tropea) to teach. Will you know in June?
I admit I do not remember Birgit because we met more than one in
Pisa. If she is studying in the Scuola or Universita' she should be
able to send your email to me, or a-sax via my Dipartimento. Vy email,_C
(un'altra volta)i chung a math.atanford.edu.
See you-all soon: Nuocia, Alessandroe tu.

^^i ^ ^7

Dipartimento di sci, 02:09 PM 5/7/97 +, contact

Date: Wed, 07 May 1997 14:09:18 +0100 (MET)
Date-warning: Date header was inserted by CESIT1.UNIFI.IT
From: sciant@CESITL.UNIFI.IT (Dipartimento di science =?UNKNOWN?Q?dell=27antichit=EO?=)
Subject: contact
X-Sender: sciant@cesitl.unifi.it
To: chung@gauss.Stanford.EDU

Caro prof. Chung,
non so se ha gii ricevuto la mia letter. Sono felicissimo che verri a
giugno a Pisa, cosi ci potremo rivedere e andare insieme a Volterra. Mia
moglie ed Alessandro stanno bene, io sto finendo una borsa post-dottorato a
Firenze. Mi comunichi la data del suo arrivo a Pisa. Verr6 a prenderla
all'aeroporto.

Affettuosi saluti
Domenico

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k7/t~$2e ./J1 00 eI Gcckl/Z4 o0 72 k z6a d"""'~~- two yx. 0 / 'p, /U,---- oo! u cxv k&- 61 ~2Rvmd 7 4" /o' ~glI~n CqTY<<>* Frwi GEORGE GREEN MEMORIAL FUND Hon. Treasurer: Chairman: Hon Secretary: Miss A Innes Professor L J Challis Miss D M Cannell Manager Department of Physics 39 Village Road National Westminster Bank The University of Nottingham Clifton The University of Nottingham Nottingham NG7 2RD Nottingham NG11 8NP Nottingham NG7 2RD Tel: (0115) 951 5132 Tel: (0115) 921 6862 Fax: (0115) 951 5187 Fax: (0115) 921 4425 e-mail: Iawrie.chaUls@nottngham.ac.uk 25 February 2000 Professor Kai Lai Chung Department of Mathematics Stanford University Stanford CAa 94305 USA Dear Professor Chung, I have been in correspondence with Professor O'Malley, of the University of Washington in Seattle. As editor-in-chief of the Classics Reprint section of S.I.A.M., he has chosen my biography of George Green, published in 1993, for the next title, due for issue in May/June. Professor O'Malley has been sending me comments on his reading associated with Green, which included your book Brown, Green and Probability, which I read in the Library here, and he referred particularly to your speculation as to whether Green and Brown ever met. I thought then that you might be interested in having a copy of the Green biography, which I am sending with my compliments. I would be prepared to say (if not to publish!) that they never did. Their life dates make it possible but Green's social circumstances really do not. Green was a victim, both of his social circumstances, which precluded association with like-minded people, and of his genius, which placed him ahead of his generation, precluding his due recognition. One may readily assume that, because of the significance of his work, he was similar in status and occupation to the numerous men of science in nineteenth century Britain, but who for some strange reason, has slipped through the net of record and recognition. It was not only the nature of his mathematical and physical concepts, but also that he was an artisa3 the world of the gentleman-scholar which impeded full dissemination of his work an_'aally his untimely death. I had not heard of Brown and Brownian motion until I had Professor O'Malley's letter. I know nothing of science and cannot understand Green's mathematics or concepts and looked up Thomas Brown in the Dictionary of Scientific Biography (1976) and found some four pages on his botanical work, association with Sir Joseph Banks, etc., and a bare ten-line paragraph with a reference to particle physics but no explanation. It was Professor Challis who gave me an explanation in terms I could reasonably understand! He has a great gift for this. Yours sincerely, Mary Cannell March 27, 2000 Miss D M Cannell 30 Village Road Clifton* Nottingham England Dear Madam: As soon as I received your letter and books I phoned OXMalley asking him to forward my thanks. I had intended to browse in your book but end- ed with reading large parts of it with much interest and great admiration. This first communication was prompted by the appearance of "The laws of Chance" on p. 109. As you notedthe names Poissons Laplace and Lagrange* not to mention Cauchy and Gauss, were referred to by Green. But apparently not DeMoivre [Newton's prot4gs], Jacques (Jakob) Berpoulli [Pho competed with Sir Isaac on a mechanics problem] who together with the first three named founded THE DOCTRINE OF CHANCEs initiated by Newton's older fratelli Pascal-Permat. So the question is: did Geo. Green realizL the import of probability in his physical researches? The "gas theory" of Boltzmann and Maxwell came soon after not to mention the quantum theory. In the preface of my book 2~ en 4srown ic) And Probability, I used a Chinese expression wondering about "h a would Green say" to this new-fangled "fortuitous" development oJ his great ideas on electricity [no longer magnetism acco1~ng to my physicisal experts]? Thank you for paying attention to my rather rhetoric question re- garding Robert Brown and Geo. Green. The former was lucky in that his botaz ic observation was soon taken up by competent mathematicians Perrin and Ein- stein. The latter actually wrote his fundamental memoir proving the exister ce of atoms moleculess?) before he had heard of Brown's pollens. Perhaps his social status, though a Scot, helped? By the ways if George Boole was hymbler than the Biller Green, being only cobblers how come he had no troub3 getting into the Roeal society? I have begun'several lectures in different countries by stating that George Green was a self-taught genius who (barely) made it to Calbridge. I was most pleased to learn from your book about his patrons and poor Jane Smith with her even children. I had not known such things happened in Eng- land of those days. Your description of COMMON ROOM scenes made me remini- sce on my days at Churchill College. Unlike the likes of Robert Murphy$ I
had champagne brought -o my rooms [what a (gre__* field outside] only once,
to entertain a guest me, on the train from Shanghai to Hangchow [Marco Polo'
Kinsai!] who claims bluer blood than the current royalty/ ... (my WUjIdAt'
Please excuse my informality and poor typing. A copy of my book will
be mailed to you in a few days. There are a number of anecdotes in it inol.
--- the symmetry of Green's functionswhich the professor gave two proofs
by electrical reciprocity. Actually it follows easily from Greenks own
formulaes as detailed in my book. My classmate in Princeton* Gilbert Agnew
Hunts improved on Green's theorem by proving the symmetry of the density of
the killed-Brownian motion. I do not like the killing but we can interpret
it as in "killing the pain".
Permit me two questions: (1) Is there a photo or portrait of Geo. Gree
(2) Does your Memorial Fund print a special edition of the great ESSAY?
Po> on p. 69v 5rd para: independentt" is French spelling
.. on p. 70s line 5: "favors" EsTc]? of. p. 67. "favorite [sic]"
Yours sincerely

Prof. Emer. Mathematics
Stanford -

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Date June 21 2000

Professor Kai Lai Chung,
903 Lathrop Drive
Stanford
CA 94305
USA

Department of
Physics
Dear Professor Kai Lai Chung,

I think you will have heard from Prof O'Malley of the sad news of Mary Cannell's
death. She died on April 18th after a short illness and last Friday there was a
Thanksgiving Service attended by 130 people followed by a Reception at the University Park
University of Nottingham at which there was an Exhibition on Green and also of Nottingham
course of Mary. NG7 2RD
UK

Mary and I worked together for 25 years initially to restore his windmill and later on Telephone
many projects including the celebration in 1993 of the 200th anniversary of his birth. I Nottingham
am very proud of the fact that she dedicated her book to me and invited me to write (0115) 951 5132
"International
something at the beginning.. She asked me to be responsible for her papers and the +44 115 951 5132
arrangements for the new edition of her biography of Green. Her family gave me the
copy of your letter to her dated March 22nd and also the copy of your book which she Facsimile
had told me about and which I have now read with great interest. I am not a theorist so (0115) 951 5187
plan to give it to my colleague Fred Sheard and look forward to his comments. +44 115 951 5187
E-mail
I was interested you spent time in Cambridge. I was a student and then lectured in ppzljc@ppnl.nott.ac.uk
Oxford before I went to Nottingham and in 1966 I1 spent 6 months in the Physics Dept
at Stanford working with Bill Little. A very enjoyable time.

Let me answer your questions. Unfortunately George Green was born just before
photography in Britain and we have not been able to find a portrait of him. It was the
tradition that all Fellows in his college would have been painted but we can only
assume that he was not a Fellow long enough for this to have happened. We have a
photo of one of his daughters but sadly not of him. You also asked if we have a
special edition of his essay. We have produced 3 volumes of his work and the first one
is his essay. However these are only photocopies of the papers with a soft cover. We
still have a few copies of a beautiful facsimile edition of his essay with a hard cover
and gold lettering. This was a set of 1000 produced by Prof Ekelof of the University
of Gothenberg nearly 50 years ago. We originally bought some from him to be resold
the profits being used towards the restoration of the Mill. Then Prof Ekelof gave us
most of the remaining copies. If you would like one of these few remaining copies I
could send you one but I am afraid I will have to ask you to send me 35 to cover the
cost and the airmail postage. (Please make the cheque payable to the George Green

Pr,-V., l 0-.a s...,u. -&- l,,a,,,-S,,rner Professor of Physics: Professor L J Challis OBE MA DPhII FnstP CPhys

Memorial Fund either in pounds or send 70$(this includes 15$ the bank charges to
convert a dollar cheque into pounds)).
With all best wishes

L J Challis

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FOREWORD

The contends of this book j divided into three terrelated parts.

Part 1 contains some of my earliest and latest e orts, plus a mixed bag

of mostly sh rt pieces on diverse themes, cho n as much by whim as by

design. In my emory they are associated th circumstances, persons and

evebts covering a pan of over sixty ye s. some of which are recalled in

the postscripts. P t 2 contains ad esses given at conferences

h-e44 in vy Part 3 contains memorials( re-

miniscences of contempor y mat ematicians and s.ae reviews of their workS

Many of them appear in the otographs at the end of the volume.,

My wife took Yhe p ns of p eparing the +he old photographs for

reproduction; it must e she who t ok the picture after the banquet in

Beijing in 1975, of which unfortunate no other souvenir could be found

despite trans-pac/fic telecommunicatio .. The last photograph of the Hill&-

gate to a Tang ynasty temple was taken b daughter Corinna in 1991, on

my 4th or 5th return to the spot after the ragic year 1937.

It is y pleasure to thank Dr. K. K. Phu founder of World Scienti-

fic Publi inh Company, whose quick and positive response made this

impromp publication possible.

May 9, 2004
Stanford, California.