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

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).

References in corpus (4)

• A characterization of dimension free concentration in terms of transportation inequalities
• A new characterization of Talagrand's transport-entropy inequalities and applications
• A note on the Modified Log-Sobolev inequality
• Modified logarithmic Sobolev inequalities on R

Cited by in corpus (4)

• Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in $L^1$
• Remark on the stability of Log-Sobolev inequality for Gaussian measure
• Transport inequalities for random point measures
• The log-Sobolev inequality for spin systems of higher order interactions