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The Wulff Crystal in Ising and Percolation Models

Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004

Paperback Engels 2006 2006e druk 9783540309888
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Samenvatting

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.

Specificaties

ISBN13:9783540309888
Taal:Engels
Bindwijze:paperback
Aantal pagina's:264
Uitgever:Springer Berlin Heidelberg
Druk:2006

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Inhoudsopgave

Phase 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.

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        The Wulff Crystal in Ising and Percolation Models