A variational approach to some transport inequalities
classification
🧮 math.PR
keywords
approachinequalitiesinequalitytransportcriticaldefinedfunctionalsimplies
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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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