Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below
L. Saloff-Coste (1994)
Colloquium Mathematicae
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L. Saloff-Coste (1994)
Colloquium Mathematicae
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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...
Gérard Ben Arous, Ofer Zeitouni (1998)
ESAIM: Probability and Statistics
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Kazuhiko Aomoto (2000)
Annales Polonici Mathematici
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The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.
B. Zegarliński (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.
Xia, Wei-Feng, Chu, Yu-Ming, Wang, Gen-Di (2010)
Abstract and Applied Analysis
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Shi, Ming-Yu, Chu, Yu-Ming, Jiang, Yue-Ping (2009)
Abstract and Applied Analysis
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Galaz-Fontes, Fernando, Sontz, Stephen Bruce (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known...