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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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.

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

First available in Project Euclid: 16 March 2011

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

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


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.

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