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

  title={Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlev{\'e} representations},
  author={Momar Dieng},
  journal={International Mathematics Research Notices},
  • M. Dieng
  • Published 18 November 2004
  • Mathematics
  • International Mathematics Research Notices
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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