Marc Yor, 1988-1996

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Title:
Marc Yor, 1988-1996
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Unknown
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English
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Yor, Marc
Chung, Kai Lai
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Box: 1
Folder: Marc Yor, 1988-1996

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Mathematics -- History -- 20th century

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Laurent SCHWARTZ
37, rue Pierre Nicole

75005 PARIS
T41. : 43 54 50 30


Paris, le 6 septembre 1988



Monsieur Marc Yor-%O
5 bis, rue Aristide Briand

91530 SAINT CHEROND














Mon cher Yorf,


Ii y a eu des difficulties assez grosses en ce qui con-
cerne le paper de Chung pour le centenaire de Paul 1 Levy ; mais
Neveu et moi-m6me sommes intervenus aupres pour que
le paper soit accept, et il l'a et6. Donc il sera public nor-
malement.


J'espere que tu as fait un bon s6jour et t'envoie mes
meilleures amiti6s.


Laurent Schwartz




Centre National de la Recherche Scientifique Universitd Pierre et Marie Curie
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October 11, 1993
Dear Yor:

Thank you for your letter from Paris which took six days ---but
it has taken me much longer to gp back to those questions we discussed.
I have now also seen p. 12 of your book with Revuz, where you had actual-
ly written the formula* oh in such a hurried and casual way as if any
redder could possibly carry out the computations (which you now showed
in detail to me in your last letter) and even less to grasp the signif i-
cance of them. I have also obtained free of charge a copy of your Zurich
lectures. If you had made me think that they were more digestible, I must
say I was deluded: though I did see things whmch look similar on the bot-
tpm of p. 41 and so forth. Half a page of explaining their relevance to
Levy's excursion theory would he/ ple like Imhof and other older read-
ers, including me. Did your .elpes
obviously younger-generation audience know such special precursors?
t Nevertheless, to e the arcsine density with the exponential densi-
tyethe way you did is a curioanty/of a certain magnitudes worthy of the
masters. Are you also conversant'with binomia&l coefficients, the general
ballot theorem ( eppli 1924), and such things? Here is a problem which
apparently nobody could solve, Let Xn be i.i.d. with
P(Xn=-a)=(b-a)/bs P(X n=b-a)=a/b, where l n with (aib)=l
Let Sn=EXk find the exact distribution of T0=min{n>l: S =0 !
n 0 n
A somewhat more general formula was given by DeMoivre*(indeedtwo formulas)
and demonstrated by Lagrange and Laplace& in the case a=l, b=2, which led
to Andrb's reflection method (which you know in BM). I found the formula
for a=l, b>2 experimentally around 1940, later confirmed by an older for-
mula due to Rothe-Schlafli-Hagen. Finally I found the probability proof
earlier this year. The problem is wide open for a>l, and nobody I consult-
ed [including the Frenchman L. Comtet whose typically Frenchs never answer-
ed; but other experts did respond] has the faintest idea. If you know a
good man or woman at these antique arts (hot really so remote from your
art), please pass it around. But don't let it trouble you if it is not
your cup of teas although it is fantastically difficult (and French).
Let me thank you again for your help although it ends in nothing.-_.j,
With best wishes .

Sincerely*
*A French protestant who had to flee to England after the Nantes edict
was revoked and so was never able to obtain a professorship.
P. S. I think I have told you before about this mistake which 99.5
per cent of French make: "enable" is not an intransitive verbs so you must
say "enables me, us, or one"s not just "enables" as in your Foreword of
the ETH book. If you do not want to be personal you can say "makes it
possible". Since I think you care for language I hope you will not be of-
fended.e (
a* ley''i's dtireff ^~e 'yak yon wi i'e








2 novembres 1993
Monsieur Yor:
J~ai fait tres mal dans le style francais. Je devrais ecriere
ST -1 1
Voici la vite preuve (pas la mienne d'alors pe l'ai trouvee depuis des
econdes)
0 = S + X mt

XTo A s --

Ceci n'est pas absolument trivial: on a besoin de quelques resultats
generals sur une promenade al6atoire recurrente. Pour cela on doit
supposed que xakxas X1 prends des valeurs entieres, et puis E(Xl) = O0
sans quoi T0 ne soit pas finite O.o,
Dans mon cas original, j'pl observe sur des dessins numeriques que
ona a
(B) O0 bn-l = a) = OP{Sbn-1 = a-b)
f ess frCc b on
ou le zero & gauche signifie la (condition "0 soit defend TABU)" --
d'ailleurs eg notation superbe: voir Note no. 2 dans mon article sur
Doeblin don't vous tenez un tirage-A-part. Dans ma derniere lettre, je
1'ai confondu (par abus d'idee) avec l'uniformit ~-de S o c
'est bizarre < je n'ai pu pas m'appercevoir la banality (A)
jusqud ce moment-ci.

J'ai vu hier soir le film "Hotel Terminus" sur TV. qui traite 1'af-
faire Klaus uarbie de Lyon Moi je suis fort impression de ce monsieur
avocat Verges. Mais il film a dure trop longtemps (3.gh.) tel que j'ai
du me coucher bien avant son fin. Est-ce que vous pouvez me dire le
verdict? Est-il vivant Barbie? Merci.


"Po '{ .









Jan. 10, 1996
Dear Yor:
I am pleased to send you the inclosure. You may recall that I asked
you [after Neveu who was, obviously, too diplomatic] to send it to Laurent.
But you refused* why? Now you must admit you were quite wrong. It pleases
me that Laurent has behaved "nicely" anS not as you and Neveu had thought
he would 3 If you want to know the 1828 thing just ask me (or him if you
dxie!) In Irish (your wife's) tongue I should claim that I (moi) did L. Sch.
a favo(u)r by writhing him that letters two or three years too late because
of you and Veveu, so that he would be able to correct the 6ad mistake and the
polytechnicians would learn properly. Let me Cmphasize that from his reply
it is clear that Aobody had (a)found the errora(b) dared to tell it him. That
can only be described as properly francaal AND NOT GOOD for your society.
A propose. since my last contact with L. Sch. [through Neveus by two tra-
nsaltantic phone calls which cost me some 50 dollars] was to ask him to over-
rule that asstwho "rejected" my memorial article for the asaine journal *
with that Jewish hippie editor (what's his name ? Ornstein said that he
"was an American Jwwv who cone red into a French Jew" [for better or worse?]
What I cannot forget- though I must by now forgive was the "comprtment" of
our other copain Paul-Andre. He ought to know (because I taught him in
Strasbourg among other things Marko'~ chains) that that ass did not have a leg
to stand on mathematically in his report" not even understanding the famous
Levy example in one case, yet he went out of his way (c'-'a-dire: gratuitous-
Lsy according-to Neveu, because they all got together and discussed the
"controversy") to support the ignorant-arrogant ads. Why? It was never
explained to me. Fortunately Laurent did the correct (and obvious) thing
which was also to his credit --- imagine if it had been Andre who would
probably make things even worse. I can never understand that behavior on
the part of Paul-Andr6e and you never explained it to me either. There is
definitely something malade in either the French character or his indivi-
dial peache. Recently* he thought I meant him by that "then young probabili-
at" wo announced that the notion of separability was Obsolete (p..87 of
my last book). Please tell him that he is wrong.
With kind regards,







July 28, 1996
Dear Yors
If you are really interested in learning about George Green's work*
you should go to the library and read the first paper in the Collected
Papers by him, reprinted by Chelsea. His (1) is what I told Laurent.
I was myself surprised that he had not known the discovery more than
100 years before him ]ihom I first met at Chevalley's office in Prince-
ton 1946/7 at which occasion he gave me his other book on exponential
sums]. As you brought up your forte the local marts, let me propose two
topics of hkstorial-technical research which occurred to me while we talked
so that we had not entirely wasted our time:
(1) Prove that Green formula by local mart. Since the answer is a Dirac
function I conjecture that this should be within the reach of marts.
(2) Prove the symmetry of Green's functions in 2 dimensions if you wi sh.
I told you a long story about this "marvellous" discovery which I shall
rename as the theorem of Green-Maxwell-Hunt. You did not seem to know Hunt
's result? Alas. "si les jeunes savent, ...". I conjecture that this can-
not be done by marts. Here is a historical comment by your grandteacher
[c'est-a-dires un maitre d'un votre propre mditres ancore vivant]. It
happened at the time when I found a minor extension of a well-kntwn re-
sult on the first exit time from a domain (par example, in R 2) and asked
you (in Berkeley then) if you knew other approaches to the problems and
you answered nol I remarked on this surprise to him and he commented
(n fact your book does not have Greene) "A book on BM without
Green's function can't be serieux [French italics mines he used a *!Iw
expression]. Please take this as a good advice from a maitre. V
Sorry I have no more spare copies to sells but you can call
Dr. Frank Ling at 1(800)2277562 World Sc. Publ. Cos in N. J.
to buy a copy if you wish. In Frances Meyer and Bru have copies which
you can borrow, provided that stupid chinois had returned Meyer's ,
In case you really read it [Meyer 40dime that he only read the Note:
the rest contains just as many curiosities!] and have any opinions it is
not too late for you to write a letter to me. Bon Tache! 2e o




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