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.
Mots clés : Logarithmic Sobolev inequality, heat kernel, Brunn-Minkowski inequality
@article{JEDP_2011____A7_0,
author = {Ledoux, Michel},
title = {Analytic and {Geometric} {Logarithmic} {Sobolev} {Inequalities}},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {7},
pages = {1--15},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2011},
doi = {10.5802/jedp.79},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.79/}
}
TY - JOUR AU - Ledoux, Michel TI - Analytic and Geometric Logarithmic Sobolev Inequalities JO - Journées équations aux dérivées partielles PY - 2011 SP - 1 EP - 15 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.79/ DO - 10.5802/jedp.79 LA - en ID - JEDP_2011____A7_0 ER -
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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