Disorder and Critical Phenomena Through Basic Probability Models [recurso electrónico] : École d’Été de Probabilités de Saint-Flour XL – 2010 / by Giambattista Giacomin.
Tipo de material: TextoSeries Lecture Notes in Mathematics ; 2025Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: XI, 130p. 12 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642211560Tema(s): Mathematics | Distribution (Probability theory) | Mathematical physics | Mathematics | Probability Theory and Stochastic Processes | Applications of Mathematics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Methods in PhysicsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 519.2 Clasificación LoC:QA273.A1-274.9QA274-274.9Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA273 .A1-274.9 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 376208-2001 |
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QA273 .A1-274.9 Random Perturbation of PDEs and Fluid Dynamic Models | QA273 .A1-274.9 Markov Decision Processes with Applications to Finance | QA273 .A1-274.9 Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model | QA273 .A1-274.9 Disorder and Critical Phenomena Through Basic Probability Models | QA273 .A1-274.9 Markov Paths, Loops and Fields | QA273 .A1-274.9 Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems | QA273 .A1-274.9 Mean Field Models for Spin Glasses |
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.
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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