The wulff crystal in ising and percolation models : Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / / Raphaël Cerf, edited by Jean Picard

• Record Nr.: UNISA996466615503316
• Autore: Cerf Raphaël
• Pubbl/distr/stampa: Germany : , : Springer, , [2006]; ©2006
• ISBN: 1-280-61834-5; 9786610618347; 3-540-34806-9
• Edizione: [1st ed. 2006.]
• Descrizione fisica: 1 online resource (266 p.)
• Collana: École d'Été de Probabilités de Saint-Flour, , 0721-5363 ; ; 1878
• Disciplina: 530.13
• Soggetti: Phase transformations (Statistical physics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.