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The Wulff crystal in Ising and percolation models : Ecole d'été de probabilités de Saint-Flour XXXIV, 2004

Author: Raphaël Cerf; Jean Picard
Publisher: Berlin : Springer, 2006.
Series: Lecture notes in mathematics (Springer-Verlag), 1878.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cerf, Raphaël.
Wulff crystal in Ising and percolation models.
Berlin : Springer, 2006
(DLC) 2006921625
(OCoLC)70104834
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Raphaël Cerf; Jean Picard
ISBN: 9783540348061 3540348069 3540309888 9783540309888 3540309268 9783540309260 1280618345 9781280618345
OCLC Number: 262691397
Notes: Cover: Blaise Pascal (1623-1662).
Description: 1 online resource (xiv, 264 pages) : illustrations.
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1878.
Responsibility: R. Cerf ; editor, Jean Picard.
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Abstract:

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  Read more...

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