Journal
PHYSICS LETTERS A
Volume 343, Issue 5, Pages 384-396Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2005.05.096
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We consider Schur function expansion for the partition function of the model of normal matrices. This expansion coincides with Takasaki's expansion 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. We also introduce Hermitian and unitary two-matrix models with generalized interaction terms in continuous and discrete versions. (c) 2005 Elsevier B.V. All rights reserved.
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