CHARACTERIZATION OF A CLASS OF WEAK TRANSPORT-ENTROPY INEQUALITIES ON THE LINE

Abstract : We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost function. As an application, we give a necessary and sufficient condition for weak transport-entropy inequalities in dimension one. In particular, we obtain a weak transport-entropy form of the convex Poincaré inequality in dimension one.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01199023
Contributor : Nathael Gozlan <>
Submitted on : Thursday, December 24, 2015 - 2:58:34 PM
Last modification on : Wednesday, July 31, 2019 - 3:24:16 PM
Long-term archiving on : Friday, March 25, 2016 - 12:00:56 PM

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  • HAL Id : hal-01199023, version 2
  • ARXIV : 1509.04202

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Yan Shu, Prasad Tetali. CHARACTERIZATION OF A CLASS OF WEAK TRANSPORT-ENTROPY INEQUALITIES ON THE LINE. Annales de l'IHP - Probabilités et Statistiques, 2018, ⟨http://imstat.org/aihp/accepted.html⟩. ⟨hal-01199023v2⟩

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