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

Giacomin, Giambattista

 
9783642211553: Disorder and Critical Phenomena Through Basic Probability Models: École d’Été de Probabilités de Saint-Flour XL – 2010
Softcover
ISBN 10: 3642211550 ISBN 13: 9783642211553
Verlag: Springer, 2011

Inhaltsangabe

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.

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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.

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Verlag
Springer
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
3642211550
ISBN 13 
9783642211553
Einband
Taschenbuch
Anzahl der Seiten
144
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