Mass transport and variants of the logarithmic Sobolev inequality

Details Mass transport and variants of the logarithmic Sobolev inequality Mass transport and variants of the logarithmic Sobolev inequality

2007-09-25

arxiv.org/abs/0709.3890v1

Mathematics

Probability

39 pages

Scientific paper

We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev case. The idea behind many of these conditions is that measures with a non-convex potential may enjoy such functional inequalities provided they have a strong integrability property that balances the lack of convexity. In addition, several known criteria are recovered in a simple unified way by transportation methods and generalized to the Riemannian setting.

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