Asymptotic Expansion of a Partition Function Related to the Sinh-model

• Main Authors: Borot, Gaëtan (Author), Guionnet, Alice (Author), Kozlowski, Karol K. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Mathematical Physics Studies,
• Subjects: Mathematics.; Potential theory (Mathematics).; System theory.; Probabilities.; Mathematical physics.; Physics.; Mathematical Physics.; Probability Theory and Stochastic Processes.; Potential Theory.; Complex Systems.; Mathematical Methods in Physics.; Statistical Physics and Dynamical Systems.

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...

Table of Contents:

• 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.