Cours SpécialisésCollection SMF 1999; 114 pp; softcover Number: 5 ISBN10: 2856290752 ISBN13: 9782856290750 List Price: US$26 Member Price: US$20.80 Order Code: COSP/5
 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 selfadjoint 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. Readership Graduate students and research mathematicians interested in operator theory and statistical physics. Table of Contents  Opérateurs autoadjoints
 Semigroupes
 Inégalités de Sobolev logarithmiques
 Mesures de Gibbs
 Stabilisation de la dynamique de Langevin
 Appendice
 Bibliographie
