A criterion for Talagrand's quadratic transportation cost inequality

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We show that the quadratic transportation cost inequality $T_2$ is equivalent to both a Poincaré 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 Poincaré inequality is satisfied.

Keywords

Probability, Functional Analysis, 47D07;60E15;60G10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/69451

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312081
 http://arxiv.org/abs/math/0312081

Collections

arXiv