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The Wulff Crystal in Ising and Percolation Models

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

  • Raphaël Cerf
  • Jean Picard

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Front Matter
      Pages 1-1
  3. Presentation of the models

    1. Front Matter
      Pages 13-13
    2. Pages 15-24
    3. Pages 25-29
  4. Main results

    1. Front Matter
      Pages 43-43
    2. Pages 45-64
  5. Large deviation principles

    1. Front Matter
      Pages 65-65
  6. Fundamental probabilistic estimates

    1. Front Matter
      Pages 103-103
    2. Pages 105-116
    3. Pages 117-127
    4. Pages 129-145
    5. Pages 147-155
  7. Basic geometric tools

    1. Front Matter
      Pages 157-157
    2. Pages 159-172
    3. Pages 173-188
    4. Pages 189-199
  8. Final steps of the proofs

    1. Front Matter
      Pages 201-201
    2. Pages 215-228
    3. Pages 229-239
    4. Pages 241-252
  9. Back Matter
    Pages 253-268

About this book

Introduction

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.

Keywords

Finite Wulff crystal ising percolation proof theorem

Authors and affiliations

  • Raphaël Cerf
    • 1
  1. 1.Mathématiques Batiment 425 UMR CNRS 8628Unversité de Paris-SudOrsay cedexFrance

Editors and affiliations

  • Jean Picard
    • 1
  1. 1.Laboratoire de Mathématiques AppliquéesUMR CNRS 6620 Université Blaise Pascal (Clermont-Ferrand)Aubière CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/b128410
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-30988-8
  • Online ISBN 978-3-540-34806-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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