The Wulff Crystal in Ising and Percolation Models [electronic resource] : Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / by Raphaël Cerf ; edited by Jean Picard.
Material type: TextSeries: Lecture Notes in Mathematics ; 1878Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XIV, 264 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540348061Subject(s): Mathematics | Mathematical optimization | Distribution (Probability theory) | Mathematical physics | Mathematics | Probability Theory and Stochastic Processes | Mathematical and Computational Physics | Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK47 |
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.
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