The Wulff crystal in Ising and percolation models : école d'été 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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| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2006. |
| Serie: | École d'Été de Probabilités de Saint-Flour
1878 |
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| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 11 janvier 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Wulff crystal in Ising and percolation models, École d'été de probabilités de Saint-Flour XXXIV, 2004, [course presented by] R. Cerf, 2006, Berlin, Springer, 1 vol. (XIV-264 p.), Lecture notes in mathematics, 978-3-540-30988-8 |
Sommario:
- 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.
- 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