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Asymptotic Expansion of a Partition Function Related to the Sinh-model
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Catalogue Information
Field name
Details
Dewey Class
530.15
Title
Asymptotic Expansion of a Partition Function Related to the Sinh-model ([EBook]) / by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski.
Author
Borot, Gaëtan
Added Personal Name
Guionnet, Alice
author.
Kozlowski, Karol K.
author.
Other name(s)
SpringerLink (Online service)
Publication
Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details
XV, 222 p. 4 illus. : online resource.
Series
Mathematical physics studies
0921-3767
ISBN
9783319333793
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-319-33379-3
Links to Related Works
Subject References:
Complex Systems
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Mathematical Methods in Physics
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Mathematical Physics
.
Mathematics
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Physics
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Potential Theory
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Potential theory (Mathematics)
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Probabilities
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Probability theory and stochastic processes
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Statistical Physics and Dynamical Systems
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System theory
.
Authors:
Borot, Gaëtan
.
Guionnet, Alice
.
Kozlowski, Karol K.
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Mathematical physics studies
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Classification:
530.15
.
530.15 (DDC 23)
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