Logarithmic Sobolev inequalities for unbounded spin systems revisited
Michel Ledoux (2001)
Séminaire de probabilités de Strasbourg
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Michel Ledoux (2001)
Séminaire de probabilités de Strasbourg
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Ivan Gentil (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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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 , 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.
Yao-Zhong Hu (2000)
Séminaire de probabilités de Strasbourg
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A. Guionnet, B. Zegarlinski (2002)
Séminaire de probabilités de Strasbourg
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Djalil Chafaï (2002)
Séminaire de probabilités de Strasbourg
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Aldéric Joulin, Nicolas Privault (2004)
ESAIM: Probability and Statistics
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We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure...
Michel Ledoux (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Radosław Adamczak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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