Analytic and Geometric Logarithmic Sobolev Inequalities
Analytic and Geometric Logarithmic Sobolev Inequalities
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.