1999/06/28 by M. Adler, P. J. Forrester, T. Nagao +1 · 1 citation
Physics and Astronomy · #solv-int #nlin.SI
paper · pdf · doi:10.1023/a:1018644606835
21 pages, no figures
arxiv created 1999/06/28 · arxiv updated 2015/06/26
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.