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Journées équations aux dérivées partielles

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Michel Ledoux
Analytic and Geometric Logarithmic Sobolev Inequalities
Journées équations aux dérivées partielles (2011), Exp. No. 7, 15 p., doi: 10.5802/jedp.79
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Class. Math.: 60H, 35K, 58J
Mots clés: Logarithmic Sobolev inequality, heat kernel, Brunn-Minkowski inequality

Résumé - Abstract

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.

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