03301nam 2200577 a 450 991048487350332120200520144314.03-642-21156-910.1007/978-3-642-21156-0(CKB)2550000000041805(SSID)ssj0000506042(PQKBManifestationID)11955273(PQKBTitleCode)TC0000506042(PQKBWorkID)10513759(PQKB)11382380(DE-He213)978-3-642-21156-0(MiAaPQ)EBC3066965(PPN)156321106(EXLCZ)99255000000004180520110705d2011 uy 0engurnn|008mamaatxtccrDisorder and critical phenomena through basic probability models Ecole d'ete de probabilites de Saint-Flour XL, 2010 /Giambattista Giacomin1st ed. 2011.New York Springer20111 online resource (XI, 130 p. 12 illus.) Lecture notes in mathematics,0075-8434 ;2025Bibliographic Level Mode of Issuance: Monograph3-642-21155-0 Includes bibliographical references and index.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.Lecture notes in mathematics (Springer-Verlag) ;2025.ProbabilitiesDistribution (Probability theory)Probabilities.Distribution (Probability theory)519.282B4460K3560K3782B2760K0582D30mscGiacomin Giambattista478956Ecole d'ete de probabilites de Saint-Flour(40th :2010)MiAaPQMiAaPQMiAaPQBOOK9910484873503321Disorder and critical phenomena through basic probability models261819UNINA