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May 2011 A new characterization of Talagrand’s transport-entropy inequalities and applications
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson
Ann. Probab. 39(3): 857-880 (May 2011). DOI: 10.1214/10-AOP570

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.

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Nathael Gozlan. Cyril Roberto. Paul-Marie Samson. "A new characterization of Talagrand’s transport-entropy inequalities and applications." Ann. Probab. 39 (3) 857 - 880, May 2011. https://doi.org/10.1214/10-AOP570

Information

Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1233.60007
MathSciNet: MR2789577
Digital Object Identifier: 10.1214/10-AOP570

Subjects:
Primary: 26D10 , 60E15 , 60F10

Keywords: concentration of measure , Hamilton–Jacobi equations , Logarithmic-Sobolev inequalities , Transport inequalities

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • May 2011
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