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By Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

This publication elaborates at the asymptotic behaviour, whilst N is big, of definite N-dimensional integrals which generally ensue in random matrices, or in 1+1 dimensional quantum integrable versions solvable via the quantum separation of variables. The creation provides the underpinning motivations for this challenge, a ancient evaluate, and a precis of the tactic, that's appropriate in larger generality. The center goals at proving a variety as much as o(1) for the logarithm of the partition functionality of the sinh-model. this can be accomplished by way of a mix of power conception and big deviation idea in an effort to clutch the best asymptotics defined by means of an equilibrium degree, the Riemann-Hilbert method of truncated Wiener-Hopf so that it will examine the equilibrium degree, the Schwinger-Dyson equations and the boostrap solution to ultimately receive a variety of correlation capabilities and the single of the partition functionality. This booklet is addressed to researchers operating in random matrices, statistical physics or integrable structures, or attracted to contemporary advancements of asymptotic research in these fields.

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Asymptotic Expansion of a Partition Function Related to the Sinh-model (Mathematical Physics Studies) by Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

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