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arXiv · 1509.04202

Characterization of a class of weak transport-entropy inequalities on the line

Nathael Gozlan·Cyril Roberto·Paul-Marie Samson·Yan Shu·Prasad Tetali
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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 Poincar{\'e} inequality in dimension one.

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Yan Shu, Prasad Tetali. 2015-09-14. Characterization of a class of weak transport-entropy inequalities on the line. https://arxiv.org/abs/1509.04202

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