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An Initiation to Logarithmic Sobolev Inequalities
 
Gilles Royer Université d’Orléans, Orléans, France
A co-publication of the AMS and the Société Mathématique de France
An Initiation to Logarithmic Sobolev Inequalities
Softcover ISBN:  978-0-8218-4401-4
Product Code:  SMFAMS/14
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
An Initiation to Logarithmic Sobolev Inequalities
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An Initiation to Logarithmic Sobolev Inequalities
Gilles Royer Université d’Orléans, Orléans, France
A co-publication of the AMS and the Société Mathématique de France
Softcover ISBN:  978-0-8218-4401-4
Product Code:  SMFAMS/14
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
  • Book Details
     
     
    SMF/AMS Texts and Monographs
    Volume: 142007; 119 pp
    MSC: Primary 60; Secondary 35; 47; 82;

    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 Société Mathématique de France. SMF members are entitled to AMS member discounts.

    Readership

    Advanced graduate students and researchers interested in mathematical statistical physics.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 142007; 119 pp
MSC: Primary 60; Secondary 35; 47; 82;

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 Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership

Advanced graduate students and researchers interested in mathematical statistical physics.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.