Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlev\'e Representations
Probability
2007-05-23 v1
Abstract
We derive Painlev\'e--type expressions for the distribution of the largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles in the edge scaling limit. The work of Johnstone and Soshnikov (see [7], [10]) implies the immediate relevance of our formulas for the largest eigenvalue of the appropriate Wishart distribution.
Cite
@article{arxiv.math/0411421,
title = {Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlev\'e Representations},
author = {Momar Dieng},
journal= {arXiv preprint arXiv:math/0411421},
year = {2007}
}