École d'Été de Probabilités de Saint-Flour

Disorder and Critical Phenomena Through Basic Probability Models

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

Authors: Giacomin, Giambattista

  • It develops the tools that allow a person with a probability background to access a large amount of theoretical physics literature.
  • Recently developed mathematical techniques are explained in detail for a class of models that demand no background beyond a standard graduate course in probability.
  • It proposes various open questions, along with the explanation of what the answer is expected to be in the physical community.
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About this book

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.

Table of contents (8 chapters)

  • Introduction

    Giacomin, Giambattista

    Pages 1-4

  • Homogeneous Pinning Systems: A Class of Exactly Solved Models

    Giacomin, Giambattista

    Pages 5-27

  • Introduction to Disordered Pinning Models

    Giacomin, Giambattista

    Pages 29-40

  • Irrelevant Disorder Estimates

    Giacomin, Giambattista

    Pages 41-50

  • Relevant Disorder Estimates: The Smoothing Phenomenon

    Giacomin, Giambattista

    Pages 51-61

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-21156-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-21155-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Disorder and Critical Phenomena Through Basic Probability Models
Book Subtitle
École d’Été de Probabilités de Saint-Flour XL – 2010
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2025
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21156-0
DOI
10.1007/978-3-642-21156-0
Softcover ISBN
978-3-642-21155-3
Series ISSN
0721-5363
Edition Number
1
Number of Pages
XI, 130
Number of Illustrations and Tables
12 b/w illustrations
Topics