%0 Journal Article
%T Classical skew orthogonal polynomials and random matrices
%A M. Adler
%A P. J. Forrester
%A T. Nagao
%A P. van Moerbeke
%J Physics
%D 1999
%I arXiv
%R 10.1023/A:1018644606835
%X Skew orthogonal polynomials arise in the calculation of the $n$-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.
%U http://arxiv.org/abs/solv-int/9907001v1