A variational approach to some transport inequalities

2015/08/30 by Fontbona, Joaquin, Gozlan, Nathael, Jabir, Jean-Francois
#26D10 #58E99 #60E15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1508.07642

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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• A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measure
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• Remark on the stability of Log-Sobolev inequality for Gaussian measure
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