The Wulff Crystal in Ising and Percolation Models [electronic resource] : Ecole d'EtȨ de ProbabilitȨs de Saint-Flour XXXIV - 2004 / by RaphaȽl Cerf ; edited by Jean Picard.
Tipo de material: TextoSeries Lecture Notes in Mathematics ; 1878 | Lecture Notes in Mathematics ; 1878Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Descripción: XIV, 264 p. online resourceTipo de contenido:- text
- computer
- online resource
- 9783540348061
- SpringerLink (Online service)
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
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.
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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