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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Michel Ledoux (1999)
Séminaire de probabilités de Strasbourg
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Patrick Cattiaux (2005)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Liming Wu (2004)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Wu, Liming, Yao, Nian (2008)
Electronic Communications in Probability [electronic only]
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Guan-Yu Chen, Wai-Wai Liu, Laurent Saloff-Coste (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.