From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality
نویسنده
چکیده
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 Rn, 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.
منابع مشابه
Logarithmic Sobolev inequality for log-concave measure from Prékopa-Leindler inequality
We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in [BL00]. We prove by Prékopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on Rn. 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...
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