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

• Κύριος συγγραφέας: Cerf, Raphaël (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Picard, Jean (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Lecture Notes in Mathematics, 1878
• Θέματα: Mathematics.; Calculus of variations.; Probabilities.; Physics.; Probability Theory and Stochastic Processes.; Theoretical, Mathematical and Computational Physics.; Calculus of Variations and Optimal Control; Optimization.

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...

Πίνακας περιεχομένων:

• 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.