An optimal double inequality for means.
Qian, Wei-Mao, Zheng, Ning-Guo (2010)
Journal of Inequalities and Applications [electronic only]
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Qian, Wei-Mao, Zheng, Ning-Guo (2010)
Journal of Inequalities and Applications [electronic only]
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Chu, Yu-Ming, Long, Bo-Yong (2010)
Abstract and Applied Analysis
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Pierre-André Zitt (2008)
ESAIM: Probability and Statistics
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In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [- (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants...
Shi, Ming-Yu, Chu, Yu-Ming, Jiang, Yue-Ping (2009)
Abstract and Applied Analysis
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Mary Beth Ruskai (1973)
Annales de l'I.H.P. Physique théorique
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D. Bakry, D. Concordet, M. Ledoux (1997)
ESAIM: Probability and Statistics
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Xia, Wei-Feng, Chu, Yu-Ming, Wang, Gen-Di (2010)
Abstract and Applied Analysis
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Sándor, József (2010)
Acta Universitatis Sapientiae. Mathematica
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Franck Barthe (2001)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Radosław Adamczak, Michał Strzelecki (2015)
Studia Mathematica
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We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev...