Analytic and Geometric Logarithmic Sobolev Inequalities

Michel Ledoux[1]

  • [1] Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse, France, and Institut Universitaire de France

Journées Équations aux dérivées partielles (2011)

  • page 1-15
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Ledoux, Michel. "Analytic and Geometric Logarithmic Sobolev Inequalities." Journées Équations aux dérivées partielles (2011): 1-15. <http://eudml.org/doc/219690>.

@article{Ledoux2011,
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.},
affiliation = {Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse, France, and Institut Universitaire de France},
author = {Ledoux, Michel},
journal = {Journées Équations aux dérivées partielles},
keywords = {Logarithmic Sobolev inequality; heat kernel; Brunn-Minkowski inequality},
language = {eng},
month = {6},
pages = {1-15},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Analytic and Geometric Logarithmic Sobolev Inequalities},
url = {http://eudml.org/doc/219690},
year = {2011},
}

TY - JOUR
AU - Ledoux, Michel
TI - Analytic and Geometric Logarithmic Sobolev Inequalities
JO - Journées Équations aux dérivées partielles
DA - 2011/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 15
AB - 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.
LA - eng
KW - Logarithmic Sobolev inequality; heat kernel; Brunn-Minkowski inequality
UR - http://eudml.org/doc/219690
ER -

References

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