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Asymptotic Expansion of a Partition Function Related to the Sinh-model (Hardcover, 1st ed. 2016)
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Asymptotic Expansion of a Partition Function Related to the Sinh-model (Hardcover, 1st ed. 2016)
Series: Mathematical Physics Studies
Expected to ship within 12 - 17 working days
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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.
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