Summary and Info
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 Sobolev inequalities with an application to a strong ergodicity 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. Titles in this series are co-published with SociÃ©tÃ© MathÃ©matique de France. SMF members are entitled to AMS member discounts.
More About the Author
Gilles Robert (born March 5, 1955) is a Canadian politician and teacher in the. Robert represented the riding of Prévost in the National Assembly of Quebec from 2008 to 2012. He is a member of the Parti Québécois.
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