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

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

2004-11-18

arxiv.org/abs/math/0411421v1

Mathematics

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Scientific paper

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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