From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Ivan Gentil[1]

  • [1] CEREMADE (UMR CNRS 7534), Université Paris-Dauphine, Place du maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 2, page 291-308
  • ISSN: 0240-2963

Abstract

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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on ℝ n , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.

How to cite

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Gentil, Ivan. "From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality." Annales de la faculté des sciences de Toulouse Mathématiques 17.2 (2008): 291-308. <http://eudml.org/doc/10087>.

@article{Gentil2008,
abstract = {We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\{\{\{\mathbb\{R\}\}\}\}^n$, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.},
affiliation = {CEREMADE (UMR CNRS 7534), Université Paris-Dauphine, Place du maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France},
author = {Gentil, Ivan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {logarithmic Sobolev inequality; convex function; measure; potential of the measure},
language = {eng},
month = {6},
number = {2},
pages = {291-308},
publisher = {Université Paul Sabatier, Toulouse},
title = {From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality},
url = {http://eudml.org/doc/10087},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Gentil, Ivan
TI - From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 2
SP - 291
EP - 308
AB - We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on ${{{\mathbb{R}}}}^n$, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.
LA - eng
KW - logarithmic Sobolev inequality; convex function; measure; potential of the measure
UR - http://eudml.org/doc/10087
ER -

References

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