15 citations · 19 across the 8 of their papers we have counts for
11 papers
On random diameters of convex bodies
O. Guedon, A. E. Litvak, K. Tatarko +1
Let be a convex body containing the origin in its interior. In this work, we study the diameters of random sections of and derive upper and lower bound…
An extension of a theorem of Chevet
Olivier Guédon, Fabien Souli
We adopt a modern approach to extend a comparison inequality of Chevet for Gaussian processes to a broader class of functions. Furthermore, we consider centered Gaussian random vec…
Talagrand's mathematical journey to the Abel Prize 2024
Olivier Guédon, Joscha Prochno
Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis…
Asymptotics of the Inertia Moments and the Variance Conjecture in Schatten Balls
Benjamin Dadoun, Matthieu Fradelizi, Olivier Guédon +1
We study the first and second orders of the asymptotic expansion, as the dimension goes to infinity, of the moments of the Hilbert-Schmidt norm of a uniformly distributed matrix in…
Random polytopes obtained by matrices with heavy tailed entries
Olivier Guédon, A. E. Litvak, K. Tatarko
Let be an random matrix with independent entries and such that in each row entries are i.i.d. Assume also that the entries are symmetric, have unit variances, and s…
On the expectation of operator norms of random matrices
Olivier Guédon, Aicke Hinrichs, Alexander E. Litvak +1
We prove estimates for the expected value of operator norms of Gaussian random matrices with independent and mean-zero entries, acting as operators from to $\ell_q^n…
Dimension free bounds for the Hardy--Littlewood maximal operator associated to convex sets
Luc Deleaval, Olivier Guédon, Bernard Maurey
This survey is based on a series of lectures given by the authors at the working seminar "Convexité et Probabilités" at UPMC Jussieu, Paris, during the spring 2013. It is devoted t…
Functional versions of L_p-affine surface area and entropy inequalities
U. Caglar, M. Fradelizi, O. Guedon +3
In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the…
Concentration phenomena in high dimensional geometry
Olivier Guédon
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view comi…
Thin-shell concentration for convex measures
Matthieu Fradelizi, Olivier Guédon, Alain Pajor
We prove that for , -concave measures on satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for the…
Moment estimates for convex measures
Radosław Adamczak, Olivier Guédon, Rafał Latała +4
Let , $\eps >0$, $r\geq (1+\eps) p$, and be a -concave random vector in with Euclidean norm . We prove that $(\E |X|^{p})^{1/{p}}\leq c (C(\eps) \E…