Last serious revision on November 18th, 2006 by B.M.
Modified on October 12th, 2024.
Modified on October 12th, 2024.
Some mathematical papers
Quelques articles mathématiques
Fifty years ago, a theorem by Xavier Fernique
on stationary Gaussian random processes (1974) has been
quite important even ouside the field of Probability.
I recall here
a proof of it, together with the necessary background
(25 pages, PDF, June 15th, 2024; modified on June 24th).
A much
longer version
(61 pages, PDF, July 1st, 2024, revised on December 8th)
contains more facts from the '70s.
Another version
(68 pages, PDF, September 29th, 2024, revised on December 9th),
with less history and more Gaussian calculations, is also provided.
Une présentation pour l'Université Gustave-Eiffel de Marne-la-Vallée en mars 2021, en version originale et en version longue.
Un texte très bavard concernant les
opérateurs sur un espace HI réel,
en exclusivité sur ce site (!)
(en français ; 44 pages, PDF, 28 juillet 2020,
revu le 17 septembre).
Entropy of spherical marginals and related inequalities,
preprint by Franck Barthe, Dario Cordero-Erausquin and B. Maurey,
(15 pages, PDF ; has appeared in
J. Math. Pures Appl. 86 (2006), 89-99).
Weakly null sequences in
L 1 ,
preprint by W.B. Johnson, B. Maurey and G. Schechtman,
(13 pages, PDF ; has appeared in
J. Amer. Math. Soc. 20 (2007), 25-36).
Easy Gaussian generic chaining
(7 pages, PDF;
posted on August 9th, 2005; last modified September 19th).
The aim of this rewriting of the "majorizing measure theorem" is to
convince the reader that the proof is, after all, relatively simple.
Easy Gaussian generic chaining, numerically oriented version
(7 pages, PDF; posted on September 13th, 2005;
last modified September 30th). This version aims to a reasonable
value of the constant involved; it is therefore not so simple
and should not be read before the "simple" version above.
Notes from a series of lectures on HI spaces
(held at Spetses, Greece, summer 1994)
I never completed this project, and I have not worked on this text since
1996; it contains therefore lots of gaps and errors.
However, a few people have mentioned these Notes in their work, so I
decided to post them here, although they are not (and probably will never
be) in decent or final form.
(93 pages, PDF)
Inégalité de Brunn-Minkowski-Lusternik, et autres
inégalités géométriques et fonctionnelles,
Séminaire Bourbaki, Novembre 2003; revised in March 2004
(19 pages, PDF)
The (B) conjecture for the Gaussian measure of dilates of symmetric
convex sets and related problems,
article by D. Cordero-Erausquin, M. Fradelizi and B. Maurey
(17 pages, PDF; December 2003 version; has appeared in
J. Funct. Anal. 214 (2004), 410-427.)
Two papers for the "Handbook of the geometry of Banach spaces"
Some remarks on isoperimetry of Gaussian type,
article by F. Barthe and B. Maurey
(14 pages, PDF;
has appeared in
Ann. IHP Probab. Stat. 36 (2000), 419-434).