Physics – Mathematical Physics
Scientific paper
2005-01-09
Physics
Mathematical Physics
21 pages, no figures. Some parts of this paper were presented on ISLAND II conference, Arran 2003
Scientific paper
10.1016/j.physleta.2005.05.096
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.
Orlov Alexander Yu.
Shiota Takahiro
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