The Annals of Probability

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

Nathael Gozlan, Cyril Roberto, and Paul-Marie Samson

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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.

Article information

Source
Ann. Probab., Volume 39, Number 3 (2011), 857-880.

Dates
First available in Project Euclid: 16 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1300281726

Digital Object Identifier
doi:10.1214/10-AOP570

Mathematical Reviews number (MathSciNet)
MR2789577

Zentralblatt MATH identifier
1233.60007

Subjects
Primary: 60E15: Inequalities; stochastic orderings 60F10: Large deviations 26D10: Inequalities involving derivatives and differential and integral operators

Keywords
Concentration of measure transport inequalities Hamilton–Jacobi equations logarithmic-Sobolev inequalities

Citation

Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie. A new characterization of Talagrand’s transport-entropy inequalities and applications. Ann. Probab. 39 (2011), no. 3, 857--880. doi:10.1214/10-AOP570. https://projecteuclid.org/euclid.aop/1300281726


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