LEADER 03977nam 22007695 450 001 9910484873503321 005 20251113194624.0 010 $a9783642211560 010 $a3642211569 024 7 $a10.1007/978-3-642-21156-0 035 $a(CKB)2550000000041805 035 $a(SSID)ssj0000506042 035 $a(PQKBManifestationID)11955273 035 $a(PQKBTitleCode)TC0000506042 035 $a(PQKBWorkID)10513759 035 $a(PQKB)11382380 035 $a(DE-He213)978-3-642-21156-0 035 $a(MiAaPQ)EBC3066965 035 $a(PPN)156321106 035 $a(EXLCZ)992550000000041805 100 $a20110714d2011 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDisorder and Critical Phenomena Through Basic Probability Models $eÉcole d?Été de Probabilités de Saint-Flour XL ? 2010 /$fby Giambattista Giacomin 205 $a1st ed. 2011. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011. 215 $a1 online resource (XI, 130 p. 12 illus.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour ;$v2025 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642211553 311 08$a3642211550 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aUnderstanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians. 410 0$aÉcole d'Été de Probabilités de Saint-Flour ;$v2025 606 $aProbabilities 606 $aMathematics 606 $aSystem theory 606 $aMathematical physics 606 $aProbability Theory 606 $aApplications of Mathematics 606 $aComplex Systems 606 $aMathematical Methods in Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aProbabilities. 615 0$aMathematics. 615 0$aSystem theory. 615 0$aMathematical physics. 615 14$aProbability Theory. 615 24$aApplications of Mathematics. 615 24$aComplex Systems. 615 24$aMathematical Methods in Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a519.2 686 $a82B44$a60K35$a60K37$a82B27$a60K05$a82D30$2msc 700 $aGiacomin$b Giambattista$0478956 712 12$aEcole d'ete de probabilites de Saint-Flour$d(40th :$f2010) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484873503321 996 $aDisorder and critical phenomena through basic probability models$9261819 997 $aUNINA