Distributions of the extreme eigenvalues of beta-Jacobi random matrices. (English) Zbl 1158.15304
Summary: 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.
MSC:
15B52 | Random matrices (algebraic aspects) |
60E05 | Probability distributions: general theory |
62H10 | Multivariate distribution of statistics |
65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |