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arXiv · 1508.07642

A variational approach to some transport inequalities

Joaquin Fontbona·Nathael Gozlan·Jean-Francois Jabir
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Abstract

We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the logarithmic Sobolev inequality implies Talagrand's transport inequality.

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Joaquin Fontbona, Nathael Gozlan, Jean-Francois Jabir. 2016-04-26. A variational approach to some transport inequalities. https://arxiv.org/abs/1508.07642

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