Stochastic proof of the sharp symmetrized Talagrand inequality

TL;DR

This paper presents a novel stochastic proof for the sharp symmetrized Talagrand inequality, utilizing a coupling based on time-reversed martingale representations to offer new insights into Gaussian functional inequalities.

Contribution

It introduces a new stochastic proof method for the sharp symmetrized Talagrand inequality using time-reversed martingale couplings, differing from previous approaches.

Findings

Provides a new stochastic proof of the inequality

Utilizes a coupling induced by time-reversed martingale representations

Enhances understanding of Gaussian functional inequalities

Abstract

We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed martingale representations.