BIRS Workshop Lecture Videos
Extreme eigenvalue distributions of some beta-Jacobi ensembles and a numerical application Dumitriu, Ioana
The beta-Jacobi ensembles complete the triad of ``classical" matrix ensembles (together with Hermite/Gaussian and Laguerre/Wishart). In the beta = 1,2,4 cases they have close relationships with the Haar orthogonal/unitary/symplectic ensembles. Although it is possible to find exact formulae for the distributions of the extreme eigenvalues of such ensembles, the are relatively opaque (involving multivariate hypergeometric functions) and not very practical. We will show a few cases where relatively simple asymptotics can be deduced from these formulae, and show a surprising numerical application.
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