Schur function expansion for normal matrix model and associated discrete matrix models
arXiv:math-ph/0501017 · doi:10.1016/j.physleta.2005.05.096
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.
21 pages, no figures. Some parts of this paper were presented on ISLAND II conference, Arran 2003