LEADER 05119nam 22008175 450 001 9910134930903321 005 20200705024957.0 010 $a3-319-19339-2 024 7 $a10.1007/978-3-319-19339-7 035 $a(CKB)4210000000000431 035 $a(SSID)ssj0001585489 035 $a(PQKBManifestationID)16263370 035 $a(PQKBTitleCode)TC0001585489 035 $a(PQKBWorkID)14864085 035 $a(PQKB)11238385 035 $a(DE-He213)978-3-319-19339-7 035 $a(MiAaPQ)EBC5591213 035 $a(PPN)188574743 035 $a(EXLCZ)994210000000000431 100 $a20150921d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRandom Walks, Random Fields, and Disordered Systems /$fby Anton Bovier, David Brydges, Amin Coja-Oghlan, Dmitry Ioffe, Gregory F. Lawler ; edited by Marek Biskup, Ji?í ?erný, Roman Kotecký 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XIII, 239 p. 14 illus., 3 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2144 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-19338-4 327 $aAnton Bovier: From spin glasses to branching Brownian motion ? and back? -- David Brydges: The Renormalization Group and Self-AvoidingWalk -- Amin Coja-Oghlan: Phase Transitions in Discrete Structures -- Dmitry Ioffe: Multidimensional Random Polymers : A Renewal Approach -- Gregory F. Lawler and Jacob Perlman: Loop measures and the Gaussian free field. 330 $aFocusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2144 606 $aMathematical physics 606 $aPhase transitions (Statistical physics) 606 $aMathematical statistics 606 $aDiscrete mathematics 606 $aProbabilities 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aPhase Transitions and Multiphase Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P25099 606 $aProbability and Statistics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17036 606 $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aMathematical physics. 615 0$aPhase transitions (Statistical physics). 615 0$aMathematical statistics. 615 0$aDiscrete mathematics. 615 0$aProbabilities. 615 14$aMathematical Physics. 615 24$aPhase Transitions and Multiphase Systems. 615 24$aProbability and Statistics in Computer Science. 615 24$aDiscrete Mathematics. 615 24$aProbability Theory and Stochastic Processes. 676 $a519.282 700 $aBovier$b Anton$4aut$4http://id.loc.gov/vocabulary/relators/aut$0300719 702 $aBrydges$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aCoja-Oghlan$b Amin$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aIoffe$b Dmitry$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLawler$b Gregory F$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aBiskup$b Marek$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $a?erný$b Ji?í$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aKotecký$b Roman$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910134930903321 996 $aRandom walks, random fields, and disordered systems$91465286 997 $aUNINA