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＜電子ブック＞
Asymptotic Expansion of a Partition Function Related to the Sinh-model / by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
(Mathematical Physics Studies. ISSN:23523905)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	XV, 222 p. 4 illus : online resource
著者標目	*Borot, Gaëtan author Guionnet, Alice author Kozlowski, Karol K author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Probabilities LCSH:Potential theory (Mathematics) LCSH:System theory FREE:Mathematical Physics FREE:Probability Theory FREE:Potential Theory FREE:Complex Systems FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-33379-3

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