Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in Geometric and Gunctional Analysis (2000). We prove by Pr├ękopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on $\dR^n$. This inequality implies results proved by Bobkov and Ledoux, the Euclidean Logarithmic Sobolev inequality generalized in the last years and it also implies some convex logarithmic Sobolev inequalities for large entropy.
 
 
Logarithmic Sobolev inequality for log-concave measure from Pr├ękopa-Leindler inequality
GENTIL Ivan
2005-16
22-03-2005
 
Université de PARIS - DAUPHINE
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