Analytic and Geometric Logarithmic Sobolev Inequalities
Journées équations aux dérivées partielles (2011), article no. 7, 15 p.

We survey analytic and geometric proofs of classical logarithmic Sobolev inequalities for Gaussian and more general strictly log-concave probability measures. Developments of the last decade link the two approaches through heat kernel and Hamilton-Jacobi equations, inequalities in convex geometry and mass transportation.

DOI: 10.5802/jedp.79
Classification: 60H, 35K, 58J
Keywords: Logarithmic Sobolev inequality, heat kernel, Brunn-Minkowski inequality
Ledoux, Michel 1

1 Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse, France, and Institut Universitaire de France
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Ledoux, Michel. Analytic and Geometric Logarithmic Sobolev Inequalities. Journées équations aux dérivées partielles (2011), article  no. 7, 15 p. doi : 10.5802/jedp.79. http://www.numdam.org/articles/10.5802/jedp.79/

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