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The Wulff Crystal in Ising and Percolation Models

Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004

  • Book
  • © 2006

Overview

Authors:
  1. Raphaël Cerf

    1. Mathématiques Batiment 425 UMR CNRS 8628, Unversité de Paris-Sud, Orsay cedex, France

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Editors:
  1. Jean Picard

    1. Laboratoire de Mathématiques Appliquées, UMR CNRS 6620 Université Blaise Pascal (Clermont-Ferrand), Aubière Cedex, France

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1878)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Phase coexistence and subadditivity

      Pages 3-12

  3. Presentation of the models

    1. Front Matter

      Pages 13-13
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    2. Ising model

      Pages 15-24

    3. Bernoulli percolation

      Pages 25-29

    4. FK or random cluster model

      Pages 31-42

  4. Main results

    1. Front Matter

      Pages 43-43
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    2. The Wulff crystal

      Pages 45-64

  5. Large deviation principles

    1. Front Matter

      Pages 65-65
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    2. Large deviation theory

      Pages 67-74

    3. Surface large deviation principles

      Pages 75-84

    4. Volume large deviations

      Pages 85-102

  6. Fundamental probabilistic estimates

    1. Front Matter

      Pages 103-103
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    2. Coarse graining

      Pages 105-116

    3. Decoupling

      Pages 117-127

    4. Surface tension

      Pages 129-145

    5. Interface estimate

      Pages 147-155

  7. Basic geometric tools

    1. Front Matter

      Pages 157-157
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    2. Sets of finite perimeter

      Pages 159-172
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Keywords

About this book

Three series of lectures were given at the 34th Probability Summer School in Saint-Flour (July 6–24, 2004), by the Professors Cerf, Lyons and Slade. We have decided to publish these courses separately. This volume contains the course of Professor Cerf. We cordially thank the author for his performance at the summer school, and for the redaction of these notes. 69 participants have attended this school. 35 of them have given a short lecture. The lists of participants and of short lectures are enclosed at the end of the volume. The Saint-Flour Probability Summer School was founded in 1971. Here are the references of Springer volumes which have been published prior to this one. All numbers refer to theLecture Notes in Mathematics series, except S-50 which refers to volume 50 of the Lecture Notes in Statistics series. 1971: vol 307 1980: vol 929 1990: vol 1527 1997: vol 1717 1973: vol 390 1981: vol 976 1991: vol 1541 1998: vol 1738 1974: vol 480 1982: vol 1097 1992: vol 1581 1999: vol 1781 1975: vol 539 1983: vol 1117 1993: vol 1608 2000: vol 1816 1976: vol 598 1984: vol 1180 1994: vol 1648 2001: vol 1837 & 1851 1977: vol 678 1985/86/87: vol 1362 & S-50 2002: vol 1840 1978: vol 774 1988: vol 1427 1995: vol 1690 2003: vol 1869 1979: vol 876 1989: vol 1464 1996: vol 1665 2004: vol 1878 & 1879 Further details can be found on the summer school web site

Authors, Editors and Affiliations

  • Laboratoire de Mathématiques Appliquées, UMR CNRS 6620 Université Blaise Pascal (Clermont-Ferrand), Aubière Cedex, France

    Jean Picard

  • Mathématiques Batiment 425 UMR CNRS 8628, Unversité de Paris-Sud, Orsay cedex, France

    Raphaël Cerf

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