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

2005/06/29 by Dieng, Momar · 3 citations
#15A52 #60F99 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.math/0506586

Abstract

We derive Painlevé--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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