Titlebook: Asymptotic Expansion of a Partition Function Related to the Sinh-model; Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski Book 2016 Springer

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0921-3767 es, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields..978-3-319-81499-5978-3-319-33379-3Series ISSN 0921-3767 Series E-ISSN 2352-3905

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Book 2016 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..

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

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,Asymptotic Expansion of ,—The Schwinger–Dyson Equation Approach,inally, upon integrating the relation (.) so as to to interpolate the partition function between a Gaussian and a general potential, we will get the .-dependent large-. asymptotic expansion of . in Proposition ..

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,The Riemann–Hilbert Approach to the Inversion of ,,n of this vector problem demands the resolution of a . matrix Riemann–Hilbert problem for an auxiliary matrix .. We construct the solution to this problem, for .-large enough, in Section . and then exhibit some of the overall properties of the solution . in Section .. We shall build on these results

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The Operators , ,ection . we shall build on this decomposition so as to show that there arise two regimes for the large-. asymptotic behaviour of . namely when.In addition to providing the associated asymptotic expansions, we shall also establish certain properties of the remainders which will turn out to be crucial

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