The Wulff Crystal in Ising and Percolation Models Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 /

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 whic...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cerf, Raphaël (Autor)
Autor Corporativo: SpringerLink (Online service)
Otros Autores: Picard, Jean (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2006.
Edición:1st ed. 2006.
Colección:École d'Été de Probabilités de Saint-Flour ; 1878
Temas:
Probabilities.
Mathematical physics.
Mathematical optimization.
Calculus of variations.
Probability Theory.
Theoretical, Mathematical and Computational Physics.
Calculus of Variations and Optimization.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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