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Journal Articles Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Year : 2018

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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Dates and versions

hal-01199023 , version 1 (14-09-2015)
hal-01199023 , version 2 (24-12-2015)

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Cite

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'Institut Henri Poincaré (B) Probabilités et Statistiques, 2018, 54 (3), pp.1667-1693. ⟨hal-01199023v2⟩
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