The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004
Title:
The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004
Author:
Cerf, Raphaël. author.
ISBN:
9783540348061
Personal Author:
Physical Description:
XIV, 264 p. online resource.
Series:
Lecture Notes in Mathematics, 1878
Contents:
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.
Abstract:
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.
Added Author:
Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/b128410