A criterion for Talagrand's quadratic transportation cost inequality
Probability
2007-05-23 v3 Functional Analysis
Abstract
We show that the quadratic transportation cost inequality is equivalent to both a Poincar\'e inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux \cite{BL97}, that are shown to hold as soon as a Poincar\'e inequality is satisfied.
Keywords
Cite
@article{arxiv.math/0312081,
title = {A criterion for Talagrand's quadratic transportation cost inequality},
author = {Patrick Cattiaux and Arnaud Guillin},
journal= {arXiv preprint arXiv:math/0312081},
year = {2007}
}