  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.
