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Characterization of Talagrand’s transport-entropy inequalities in metric spaces. (English) Zbl 1283.60029
The authors establish that a modified log-Sobolev inequality implies the corresponding transport-entropy inequality, thus extending a classical result of Otto and Villani. As main result they obtain the equivalence of the transport-entropy inequality with a modified log-Sobolev inequality called \((\tau)\)-log Sobolev inequality. As an application it is deduced that these inequalities remain stable under perturbations (Holley-Stroock perturbation result).

MSC:
60E15 Inequalities; stochastic orderings
26D10 Inequalities involving derivatives and differential and integral operators
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