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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.

By: Cerf, Raphaël [author.].
Contributor(s): Picard, Jean [editor.] | SpringerLink (Online service).
Material type: TextTextSeries: École d'Été de Probabilités de Saint-Flour: 1878Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XIV, 264 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540348061.Subject(s): Distribution (Probability theory | Mathematical optimization | Probability Theory and Stochastic Processes | Theoretical, Mathematical and Computational Physics | Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 519.2 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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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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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