Random surfaces / Scott Sheffield

Auteur: Sheffield, Scott (1973-) - AuteurType de document: MonographieCollection: Astérisque ; 304Langue: anglaisPays: FranceÉditeur: Paris : Société Mathématique de France, 2005Description: 1 vol. (VI-175 p.) ; 24 cm ISBN: 9782856291870 ; br. Note: This treatise, which is the author's thesis, gives an authorative description of lattice models of random surfaces modelled by “gradient Gibbs measures”. These gradient Gibbs measures are defined on observables in which the height of the surface is divided out. This height can be either discrete-valued or have values in the continuum. In cases where the surface fluctuates too strongly and cannot be described by a Gibbs measure, gradient Gibbs measure, which then are “rough” (as opposed to the “smooth” case, where one has the restriction of proper Gibbs measures), still may exist. In some cases uniqueness results for surfaces of a given slope may be obtained. Although these gradient Gibbs measures had been introduced before, Sheffield's work is a very valuable addition to the literature, both as a careful review of the general theory, describing gradient Gibbs measures, large deviation principles and variational principles, and at the same time containing various new results of interest for more specific classes of models. (Zentralblatt)Bibliographie: Bibliogr. p.169-175. Sujets MSC: 60D05 Probability theory and stochastic processes -- Geometric probability and stochastic geometry -- Geometric probability and stochastic geometry
60F10 Probability theory and stochastic processes -- Limit theorems -- Large deviations
60G60 Probability theory and stochastic processes -- Stochastic processes -- Random fields
82B20 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Random walks, random surfaces, lattice animals, etc
En-ligne: Résumé
Location Call Number Status Date Due
Couloir 03922-01 / Séries SMF 304 (Browse Shelf) Available

This treatise, which is the author's thesis, gives an authorative description of lattice models of random surfaces modelled by “gradient Gibbs measures”. These gradient Gibbs measures are defined on observables in which the height of the surface is divided out. This height can be either discrete-valued or have values in the continuum. In cases where the surface fluctuates too strongly and cannot be described by a Gibbs measure, gradient Gibbs measure, which then are “rough” (as opposed to the “smooth” case, where one has the restriction of proper Gibbs measures), still may exist. In some cases uniqueness results for surfaces of a given slope may be obtained. Although these gradient Gibbs measures had been introduced before, Sheffield's work is a very valuable addition to the literature, both as a careful review of the general theory, describing gradient Gibbs measures, large deviation principles and variational principles, and at the same time containing various new results of interest for more specific classes of models. (Zentralblatt)

Bibliogr. p.169-175

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