The Wulff Crystal in Ising and Percolation Models

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Ecole d’Eté de Probabilités de Saint-Flour XXXIV – 2004, Lecture Notes in Mathematics 1878 – École d’Été de Probabilités de Saint-Flour

ISBN: 3540309888
ISBN 13: 9783540309888
Autor: Cerf, Raphaël
Herausgeber: Jean Picard
Verlag: Springer Verlag GmbH
Umfang: xiv, 264 S., 32 s/w Illustr.
Erscheinungsdatum: 12.05.2006
Auflage: 1/2006
Produktform: Kartoniert
Einband: KT

InhaltsangabePhase coexistence and subadditivity.- Presentation of the models.- Ising model.- Bernoulli percolation.- FK or random cluster model.- Main results.- The Wulff crystal.- Large deviation principles.- Large deviation theory.- Surface large deviation principles.- Volume large deviations.- Fundamental probabilistic estimates.- Coarse graining.- Decoupling.- Surface tension.- Interface estimate.- Basic geometric tools.- Sets of finite perimeter.- Surface energy.- The Wulff theorem.- Final steps of the proofs.- LDP for the cluster shapes.- Enhanced upper bound.- LDP for FK percolation.- LDP for Ising.

Beschreibung

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

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