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

Nathael Gozlan 1 Cyril Roberto 1 Paul-Marie Samson 1
1 Laboratoire d'Analyse et de Mathématiques Appliquées
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
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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https://hal-upec-upem.archives-ouvertes.fr/hal-00795826
Contributor : Nathael Gozlan <>
Submitted on : Friday, March 1, 2013 - 2:23:39 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson. A new characterization of Talagrand's transport-entropy inequalities and applications. Annals of Probability, Institute of Mathematical Statistics, 2011, 39 (3), pp.857--880. ⟨10.1214/10-AOP570⟩. ⟨hal-00795826⟩

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