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arXiv · 0709.3890

Mass transport and variants of the logarithmic Sobolev inequality

Franck Barthe·Alexander V. Kolesnikov
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Abstract

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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Franck Barthe, Alexander V. Kolesnikov. 2007-09-25. Mass transport and variants of the logarithmic Sobolev inequality. https://arxiv.org/abs/0709.3890

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