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.
@article{JEDP_2011____A7_0,
author = {Ledoux, Michel},
title = {Analytic and Geometric Logarithmic Sobolev Inequalities},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {2011},
pages = {1-15},
doi = {10.5802/jedp.79},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_2011____A7_0}
}
Ledoux, Michel. Analytic and Geometric Logarithmic Sobolev Inequalities. Journées équations aux dérivées partielles, (2011), pp. 1-15. doi : 10.5802/jedp.79. http://gdmltest.u-ga.fr/item/JEDP_2011____A7_0/
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