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Asymptotic expansion of a partition function related to the sinh-model / / by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski



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Autore: Borot Gaëtan Visualizza persona
Titolo: Asymptotic expansion of a partition function related to the sinh-model / / by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Edizione: 1st ed. 2016.
Descrizione fisica: 1 online resource (XV, 222 p. 4 illus.)
Disciplina: 510
Soggetto topico: Mathematical physics
Probabilities
Potential theory (Mathematics)
Statistical physics
Dynamical systems
Physics
Mathematical Physics
Probability Theory and Stochastic Processes
Potential Theory
Complex Systems
Mathematical Methods in Physics
Statistical Physics and Dynamical Systems
Persona (resp. second.): GuionnetAlice
KozlowskiKarol K
Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
Nota di contenuto: Introduction -- 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.
Sommario/riassunto: This 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.
Titolo autorizzato: Asymptotic Expansion of a Partition Function Related to the Sinh-model  Visualizza cluster
ISBN: 3-319-33379-8
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910155305503321
Lo trovi qui: Univ. Federico II
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Serie: Mathematical Physics Studies, . 0921-3767