Borot G., Guionnet A., Kozlowski K.K. Asymptotic Expansion of a Partition Function Related to the Sinh-model

Springer International Publishing, Switzerland, 2016. — 233 p. — (Mathematical Physics Studies) — ISBN: 978-3-319-33378-6The present work develops techniques enabling one to carry out the largeN asymptotic analysis of a class of multiple integrals that arise as representations for the correlation functions in quantum integrable models solvable by the quantum separation of variables.
The main task of the book is to develop an effective method of asymptotic analysis of the rescaled multiple integral Z N [V] in the case when TN = Na, 0a1/6 and V is a given N-independent strictly convex smooth function satisfying to a few additional technical hypothesis.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 UN-1
Asymptotic Analysis of Integrals
Appendixes
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