The Wulff Crystal in Ising and Percolation Models
Cerf, Raphaël.
The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Raphaël Cerf ; edited by Jean Picard. - XIV, 264 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1878 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1878 .
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.
9783540348061
10.1007/b128410 doi
Distribution (Probability theory.
Mathematical optimization.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
Calculus of Variations and Optimal Control; Optimization.
QA273.A1-274.9 QA274-274.9
519.2
The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Raphaël Cerf ; edited by Jean Picard. - XIV, 264 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1878 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1878 .
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.
9783540348061
10.1007/b128410 doi
Distribution (Probability theory.
Mathematical optimization.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
Calculus of Variations and Optimal Control; Optimization.
QA273.A1-274.9 QA274-274.9
519.2