From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Ivan Gentil (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Prékopa-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.

Domaines: Probabilités [math.PR]

Ivan Gentil. From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2008, Sér. 6, 17 (2), pp.291-308. ⟨hal-00008521v4⟩