The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 /

• Main Author: Cerf, Raphaël (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Picard, Jean (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1878
• Subjects: Mathematics.; Calculus of variations.; Probabilities.; Physics.; Probability Theory and Stochastic Processes.; Theoretical, Mathematical and Computational Physics.; Calculus of Variations and Optimal Control; Optimization.

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 whic...

Table of 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.