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Two-matrix model with semiclassical potentials and extended Whitham hierarchy

M. Bertola
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Abstract

We consider the two-matrix model with potentials whose derivative are arbitrary rational function of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard-edges). We derive an explicit formula for the planar limit of the free energy and we derive a calculus which allows to compute derivatives of arbitrarily high order by extending classical Rauch's variational formulae. The four-points correlation functions are explicitly worked out. The formalism extends naturally to the computation of residue formulae for the tau function of the so-called universal Whitham hierarchy studied mainly by I. Krichever: our setting extends that moduli space in that there are certain extra data.

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M. Bertola. 2005-11-29. Two-matrix model with semiclassical potentials and extended Whitham hierarchy. https://doi.org/10.1088/0305-4470%2F39%2F28%2Fs05

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