A Riemann-Hilbert problem for skew-orthogonal polynomials
复变函数
2007-05-23 v3 数学物理
math.MP
摘要
We find a local Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree . Our Riemann-Hilbert problem is similar to a local Riemann-Hilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polynomials. This gives more motivation for finding methods to compute asymptotics of high order Riemann-Hilbert problems, and brings us closer to finding asymptotics of the skew-orthogonal polynomials.
引用
@article{arxiv.math/0610592,
title = {A Riemann-Hilbert problem for skew-orthogonal polynomials},
author = {V. U. Pierce},
journal= {arXiv preprint arXiv:math/0610592},
year = {2007}
}
备注
9 pages, v. 2 fixed some typos, v. 3 revised proof