Schur function expansion for normal matrix model and associated discrete matrix models
数学物理
2009-11-11 v1 math.MP
摘要
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.
引用
@article{arxiv.math-ph/0501017,
title = {Schur function expansion for normal matrix model and associated discrete matrix models},
author = {A. Yu. Orlov and T. Shiota},
journal= {arXiv preprint arXiv:math-ph/0501017},
year = {2009}
}
备注
21 pages, no figures. Some parts of this paper were presented on ISLAND II conference, Arran 2003