English

A new characterization of Talagrand's transport-entropy inequalities and applications

Probability 2011-04-08 v1

Abstract

We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.

Keywords

Cite

@article{arxiv.1104.1303,
  title  = {A new characterization of Talagrand's transport-entropy inequalities and applications},
  author = {Nathael Gozlan and Cyril Roberto and Paul-Marie Samson},
  journal= {arXiv preprint arXiv:1104.1303},
  year   = {2011}
}

Comments

Published in at http://dx.doi.org/10.1214/10-AOP570 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)