Disorder and Critical Phenomena Through Basic Probability Models

École d’Été de Probabilités de Saint-Flour XL – 2010

  • Giambattista Giacomin

Part of the Lecture Notes in Mathematics book series (LNM, volume 2025)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 2025)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Giambattista Giacomin
    Pages 1-4
  3. Giambattista Giacomin
    Pages 29-40
  4. Giambattista Giacomin
    Pages 41-50
  5. Giambattista Giacomin
    Pages 51-61
  6. Giambattista Giacomin
    Pages 63-90
  7. Giambattista Giacomin
    Pages 91-99
  8. Giambattista Giacomin
    Pages 101-112
  9. Back Matter
    Pages 113-130

About this book

Introduction

Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.

Keywords

82B44; 60K35; 60K37; 82B27; 60K05; 82D30 critical phenomena disorder localization renewal processes statistical mechanics

Authors and affiliations

  • Giambattista Giacomin
    • 1
  1. 1.Département de MathématiquesUniversité Paris DiderotParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21156-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21155-3
  • Online ISBN 978-3-642-21156-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book