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Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlevé Representations

Momar Dieng
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Abstract

We derive Painlevé--type expressions for the distribution of the $m^{th}$ 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 $m^{th}$ largest eigenvalue of the appropriate Wishart distribution.

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Momar Dieng. 2004-11-18. Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlevé Representations. https://arxiv.org/abs/math/0411421

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