Limit Theorems for Beta-Jacobi Ensembles

Details Limit Theorems for Beta-Jacobi Ensembles Limit Theorems for Beta-Jacobi Ensembles

2009-11-11

arxiv.org/abs/0911.2262v1

Mathematics

Probability

Scientific paper

For a beta-Jacobi ensemble determined by parameters a_1, a_2 and n, under the restriction that the three parameters go to infinity with n and a_1 being of small orders of a_2, we obtain both the bulk and the edge scaling limits. In particular, we derive the asymptotic distributions for the largest and the smallest eigenvalues, the Central Limit Theorems of the eigenvalues, and the limiting distributions of the empirical distributions of the eigenvalues.

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