Distributions of the Extreme Eigenvaluesof Beta-Jacobi Random Matrices

Authors:
Ioana Dumitriu;Plamen Koev
Affiliations:
dumitriu@math.washington.edu;plamen@math.mit.edu
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2008

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Abstract

We present explicit formulas for the distributions of the extreme eigenvalues of the $\beta$-Jacobi random matrix ensemble in terms of the hypergeometric function of a matrix argument. For $\beta=1,2,4,$ these formulas specialize to the well-known real, complex, and quaternion Jacobi ensembles, respectively.