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Une Initiation aux Inégalités de Sobolev Logarithmiques
Gilles Royer, Université d'Orléans, France
A publication of the Société Mathématique de France.
Cours Spécialisés--Collection SMF
1999; 114 pp; softcover
Number: 5
ISBN-10: 2-85629-075-2
ISBN-13: 978-2-85629-075-0
List Price: US$26
Member Price: US$20.80
Order Code: COSP/5
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The book starts with an introduction to logarithmic Sobolev inequalities. Then the author shows how these inequalities are used in mathematical statistical physics to prove the ergodicity of certain unbounded lattice spins systems with weak interactions. Only a narrow angle in the wide domain of Gibbs measures is considered in the book, but it is an important development by B. Zegarlinski of one of R. L. Dobrushin's fundamental ideas about describing a random field in terms of conditional probablities. The book provides most of the required basic notions, such as self-adjoint operators, diffusion processes and Gibbs measures. Some complements and exercises are also provided.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in operator theory and statistical physics.

Table of Contents

  • Opérateurs autoadjoints
  • Semi-groupes
  • Inégalités de Sobolev logarithmiques
  • Mesures de Gibbs
  • Stabilisation de la dynamique de Langevin
  • Appendice
  • Bibliographie
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