English

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 mthm^{th} 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 mthm^{th} largest eigenvalue of the appropriate Wishart distribution.

Keywords

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}
}