TY  - BOOK
AU  - Cerf,Raphaël
AU  - Picard,Jean
ED  - SpringerLink (Online service)
TI  - The Wulff Crystal in Ising and Percolation Models: Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 
T2  - Lecture Notes in Mathematics,
SN  - 9783540348061
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2006///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Mathematical optimization
KW  - Distribution (Probability theory)
KW  - Mathematical physics
KW  - Probability Theory and Stochastic Processes
KW  - Mathematical and Computational Physics
KW  - Calculus of Variations and Optimal Control; Optimization
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b128410
ER  -