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

  • Author(s): Dieng, Momar
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0506586.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. This work generalizes to general $m$ the $m=1$ results of Tracy and Widom [23]. The results of Johnstone and Soshnikov (see [15], [19]) imply the immediate relevance of our formulas for the $m^{th}$ largest eigenvalue of the appropriate Wishart distribution.

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