LEADER 04493nam 22007575 450 001 9910484873503321 005 20200706173447.0 010 $a3-642-21156-9 024 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 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2025 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-21155-0 320 $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,$x0721-5363 ;$v2025 606 $aProbabilities 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aStatistical physics 606 $aDynamical systems 606 $aPhysics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aProbabilities. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aPhysics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aApplications of Mathematics. 615 24$aComplex Systems. 615 24$aMathematical Methods in Physics. 615 24$aStatistical Physics and Dynamical Systems. 676 $a519.2 686 $a82B44$a60K35$a60K37$a82B27$a60K05$a82D30$2msc 700 $aGiacomin$b Giambattista$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478956 712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(40th :$f2010) 906 $aBOOK 912 $a9910484873503321 996 $aDisorder and critical phenomena through basic probability models$9261819 997 $aUNINA