# Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlevé representations

@article{Dieng2005DistributionFF, title={Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlev{\'e} representations}, author={Momar Dieng}, journal={International Mathematics Research Notices}, year={2005}, volume={2005}, pages={2263-2287} }

Author(s): Dieng, Momar | Abstract: We derive Painlev #x27;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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