Une initiation aux inégalités de Sobolev logarithmiques / Gilles Royer
Type de document : MonographieCollection : Cours spécialisés, 5Langue : français.Pays: France.Éditeur : Paris : Société Mathématique de France, 1999Description : 1 vol. (114 p.) : ill. ; 24 cmISBN: 9782856290750.ISSN: 1284-6090.Bibliographie : Bibliogr. p. [111]-114.Sujet MSC : 47A35, Operator theory - General theory of linear operators, Ergodic theory of linear operators60J60, Probability theory and stochastic processes - Markov processes, Diffusion processes
60K35, Probability theory and stochastic processes - Special processes, Interacting random processes; statistical mechanics type models; percolation theory
82C20, Statistical mechanics, structure of matter, Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanicsEn-ligne : Résumé
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries COSP (Browse shelf(Opens below)) | Available | 08107-01 |
Bibliogr. p. [111]-114
This course is an introduction to logarithmic Sobolev inequalities aiming at presenting how they are used to prove the ergodicity of unbounded spin systems under weak interaction. This kind of models was considered in the context of field theory, where E. Nelson proved the hypercontractivity property which L. Gross motivated to introduce logarithmic Sobolev inequalities. The unboundedness of the spins introduces technical difficulties, but leads to use more varied tools. Only a narrow angle in the domain of Gibbs measures is considered, but it is an important development by B. Zegarlinski of one of R. L. Dobrushin's fundamental ideas. The course also provides the basic notions needed for diffusion processes (as self-adjoint operators) and Gibbs measures. Complements and exercises help to enlarge the domain dealt with. (Zentralblatt)
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