Classical skew orthogonal polynomials and random matrices
solv-int
2015-06-26 v1 可精确求解与可积系统
摘要
Skew orthogonal polynomials arise in the calculation of the -point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the cases that the eigenvalue probability density function involves a classical weight function, explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials, and the structure is used to give a closed form expression for the sum. This theory treates all classical cases on an equal footing, giving formulas applicable at once to the Hermite, Laguerre and Jacobi cases.
引用
@article{arxiv.solv-int/9907001,
title = {Classical skew orthogonal polynomials and random matrices},
author = {M. Adler and P. J. Forrester and T. Nagao and P. van Moerbeke},
journal= {arXiv preprint arXiv:solv-int/9907001},
year = {2015}
}
备注
21 pages, no figures