| Document Type
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BL
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| Record Number
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1005182
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| Doc. No
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b759552
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| Uniform Title
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Initiation aux inégalités de Sobolev logarithmiques.English
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| Main Entry
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Royer, Gilles.
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| Title & Author
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An initiation to logarithmic Sobolev inequalities /\ Gilles Royer ; translated by Donald Babbitt.
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, ©2007.
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| Series Statement
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Cours spécialisés,; 5
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SMF/AMS texts and monographs,; v. 14
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| Page. NO
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viii, 119 pages ;; 26 cm.
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| ISBN
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0821844016
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: 9780821844014
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| Bibliographies/Indexes
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Includes bibliographical references (pages 117-119).
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| Contents
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Self-adjoint operators -- Symmetric operators -- Spectral decomposition of self-adjoint operators -- Semi-groups -- Semi-groups of self-adjoint operators -- Kolmogorov semi-groups -- Logarithmic Sobolev inequalities -- The Poincaré and gross inequalities -- An application to ergodicity -- Gibbs measures -- Generalities -- An Ising model with real spin -- Stabilization of Glauber-Langevin dynamics -- The gross inequality and stabilization -- The case of weak interactions -- Perspectives -- Appendix A -- Markovian kernels -- Bounded real measures -- The topology of weak convergence.
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| Abstract
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"This book provides an introduction to logarithmic Sobolev inequalities with some important applications to mathematical statistical physics. Royer begins by gathering and reviewing the necessary background material on selfadjoint operators, semigroups, Kolmogorov diffusion processes, solutions of stochastic differential equations, and certain other related topics. There then is a chapter on log Sololev inequalities with an application to a strong erogicity theorem for Kolmogorov diffusion processes. The remaining two chapters consider the general setting for Gibbs measures including existence and uniqueness issues, the Ising model with real spins and the application of log Sobolev inequalities to show the stabilization of the Glauber-Langevin dynamic stochastic models for the Ising model with real spins. The exercises and complements extend the material in the main text to related areas such as Markov chains."--Jacket.
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| Subject
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Differential inequalities.
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Ergodic theory.
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Logarithmic functions.
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Semigroups of operators.
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31.46 functional analysis.
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| Subject
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Differential inequalities.
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| Subject
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Differential inequalities.
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Ergodic theory.
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Ergodic theory.
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Ising model.
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Logarithmic functions.
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Semigroups of operators.
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Semigroups of operators.
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Stochastic differential equations.
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| Dewey Classification
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515/.48
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| LC Classification
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QA313.R6913 2007
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| NLM classification
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31.46bcl
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31.46.bcl
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