219 citations · 483 across the 21 of their papers we have counts for
24 papers
A Gaussian correlation inequality for plurisubharmonic functions
Franck Barthe, Dario Cordero-Erausquin
A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs ar…
Volumes of subset Minkowski sums and the Lyusternik region
Franck Barthe, Mokshay Madiman
We begin a systematic study of the region of possible values of the volumes of Minkowski subset sums of a collection of compact sets in , which we call the Lyuste…
Volume properties of high-dimensional Orlicz balls
Franck Barthe, P Wolff
We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an application, we describe a large family of Orlicz balls which verify a famous con…
Functional inequalities for two-level concentration
Franck Barthe, Michal Strzelecki
Probability measures satisfying a Poincar{é} inequality are known to enjoy a dimension free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux…
Spectral gaps, symmetries and log-concave perturbations
Franck Barthe, Bo'az Klartag
We discuss situations where perturbing a probability measure on does not deteriorate its Poincaré constant by much. A particular example is the symmetric exponential…
Positive Gaussian kernels also have Gaussian minimizers
Franck Barthe, Pawel Wolff
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constan…