On the convex infimum convolution inequality with optimal cost function

Abstract

We show that every symmetric random variable with log-concave tails satisfies the convex infimum convolution inequality with an optimal cost function (up to scaling). As a result, we obtain nearly optimal comparison of weak and strong moments for symmetric random vectors with independent coordinates with log-concave tails.

11 pages

References in corpus (3)

• Comparison of weak and strong moments for vectors with independent coordinates
• A characterization of a class of convex log-Sobolev inequalities on the real line
• A note on the convex infimum convolution inequality