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Schur function expansion for normal matrix model and associated discrete matrix models

A. Yu. Orlov·T. Shiota
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Abstract

We consider Schur function expansion for the partition function of the model of normal matrices. We show that this expansion coincides with Takasaki expansion \cite{Tinit} for tau functions of Toda lattice hierarchy. We show that the partition function of the model of normal matrices is, at the same time, a partition function of certain discrete models, which can be solved by the method of orthogonal polynomials. We obtain discrete versions of various known matrix models: models of non-negative matrices, unitary matrices, normal matrices.

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A. Yu. Orlov, T. Shiota. 2005-01-09. Schur function expansion for normal matrix model and associated discrete matrix models. https://doi.org/10.1016/j.physleta.2005.05.096

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