Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlev<metaTags></metaTags>#x27;e Representations
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Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlev e Representations

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https://arxiv.org/pdf/math/0411421.pdf
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Abstract

We derive Painlev e--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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