LEADER 04630nam 22007455 450 001 9910155305503321 005 20220418232643.0 010 $a3-319-33379-8 024 7 $a10.1007/978-3-319-33379-3 035 $a(CKB)4340000000024354 035 $a(DE-He213)978-3-319-33379-3 035 $a(MiAaPQ)EBC4768144 035 $a(PPN)197455417 035 $a(EXLCZ)994340000000024354 100 $a20161210d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic expansion of a partition function related to the sinh-model$b[electronic resource] /$fby Gaėtan Borot, Alice Guionnet, Karol K. Kozlowski 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XV, 222 p. 4 illus.) 225 1 $aMathematical Physics Studies,$x0921-3767 311 $a3-319-33378-X 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aIntroduction -- Main results and strategy of proof -- Asymptotic expansion of ln ZN[V], the Schwinger-Dyson equation approach -- The Riemann?Hilbert approach to the inversion of SN -- The operators WN and U-1N -- Asymptotic analysis of integrals -- Several theorems and properties of use to the analysis -- Proof of Theorem 2.1.1 -- Properties of the N-dependent equilibrium measure -- The Gaussian potential -- Summary of symbols. 330 $aThis book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core  aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields. 410 0$aMathematical Physics Studies,$x0921-3767 606 $aMathematical physics 606 $aProbabilities 606 $aPotential theory (Mathematics) 606 $aStatistical physics 606 $aDynamical systems 606 $aPhysics 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 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$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aMathematical physics. 615 0$aProbabilities. 615 0$aPotential theory (Mathematics). 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aPhysics. 615 14$aMathematical Physics. 615 24$aProbability Theory and Stochastic Processes. 615 24$aPotential Theory. 615 24$aComplex Systems. 615 24$aMathematical Methods in Physics. 615 24$aStatistical Physics and Dynamical Systems. 676 $a510 700 $aBorot$b Gaėtan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755840 702 $aGuionnet$b Alice$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKozlowski$b Karol K$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910155305503321 996 $aAsymptotic Expansion of a Partition Function Related to the Sinh-model$92108049 997 $aUNINA