# Une Initiation aux Inégalités de Sobolev Logarithmiques

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*Gilles Royer*

A publication of the Société Mathématique de France

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.

#### Readership

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