From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Details From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

2007-10-26

arxiv.org/abs/0710.5025v1

Mathematics

Probability

Scientific paper

We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Pr\'ekopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality for all uniform strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.

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