Disorder and Critical Phenomena Through Basic Probability Models: École d’Été de Probabilités de Saint-Flour XL – 2010

Author:   Giambattista Giacomin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2011 ed.
Volume:   2025
ISBN:  

9783642211553


Pages:   130
Publication Date:   16 July 2011
Format:   Paperback
Availability:   In Print   Availability explained
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Disorder and Critical Phenomena Through Basic Probability Models: École d’Été de Probabilités de Saint-Flour XL – 2010


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Overview

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.

Full Product Details

Author:   Giambattista Giacomin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2011 ed.
Volume:   2025
Dimensions:   Width: 15.50cm , Height: 0.70cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642211553


ISBN 10:   3642211550
Pages:   130
Publication Date:   16 July 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

1 Introduction.- 2 Homogeneous pinning systems: a class of exactly solved models.- 3 Introduction to disordered pinning models.- 4 Irrelevant disorder estimates.- 5 Relevant disorder estimates: the smoothing phenomenon.- 6 Critical point shift: the fractional moment method.- 7 The coarse graining procedure.- 8 Path properties.

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