Characterization of Talagrand's transport-entropy inequalities in metric spaces

TL;DR

This paper characterizes Talagrand's transport-entropy inequalities in metric spaces and demonstrates their stability under bounded perturbations, enhancing understanding of their mathematical properties.

Contribution

It provides a new characterization of transport-entropy inequalities and proves their stability under bounded perturbations in metric spaces.

Findings

Transport-entropy inequalities are characterized in metric spaces.

These inequalities are stable under bounded perturbations.

The Holley-Stroock perturbation Lemma is applied to establish stability.

Abstract

We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation Lemma).