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)