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The Wulff Crystal in Ising and Percolation Models : Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / by Raphaël Cerf ; edited by Jean Picard.
- Format:
- Book
- Author/Creator:
- Cerf, Raphaël, author.
- Series:
- École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 1878.
- École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 1878
- Language:
- English
- Subjects (All):
- Distribution (Probability theory).
- Mathematical optimization.
- Probability Theory and Stochastic Processes.
- Theoretical, Mathematical and Computational Physics.
- Calculus of Variations and Optimal Control; Optimization.
- Local Subjects:
- Probability Theory and Stochastic Processes.
- Theoretical, Mathematical and Computational Physics.
- Calculus of Variations and Optimal Control; Optimization.
- Physical Description:
- 1 online resource (XIV, 264 pages).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
- System Details:
- text file PDF
- Summary:
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 9783540348061
- Access Restriction:
- Restricted for use by site license.
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