Deviation inequalities for convex functions motivated by the Talagrand conjecture

Abstract

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.

References in corpus (4)

• Regularization under diffusion and anti-concentration of the information content
• The Borell-Ehrhard Game
• Regularization in $L_1$ for the Ornstein--Uhlenbeck semigroup
• Hypercontractivity for log-subharmonic functions

Cited by in corpus (3)

• Hypercontractivity for Markov Semigroups
• The equality cases of the Ehrhard-Borell inequality
• Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in $L^1$