Logarithmic Sobolev inequality for log-concave measure from Prekopa-Leindler inequality

Details Logarithmic Sobolev inequality for log-concave measure from Prekopa-Leindler inequality Logarithmic Sobolev inequality for log-concave measure from Prekopa-Leindler inequality

2005-03-23

arxiv.org/abs/math/0503476v1

Mathematics

Functional Analysis

Scientific paper

We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in GAFA (2000). We prove by Prekopa-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.

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