Deviation inequalities for convex functions motivated by the Talagrand conjecture

Nathael Gozlan, Mokshay Madiman, Cyril Roberto, Paul-Marie Samson

Published 2017-06-27Version 1

Motivated by Talagrand's conjecture on regularization properties of the natural semigroup on the Boolean hypercube, and in particular its continuous analogue involving regularization properties of the Ornstein-Uhlenbeck semigroup acting on in-tegrable functions, we explore deviation inequalities for log-semiconvex functions under Gaussian measure.