LARGE DEVIATIONS FOR TOP EIGENVALUES OF β-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Let lambda = (lambda(1), center dot center dot center dot, lambda(n)) be beta-Jacobi ensembles with parameters p(1), p(2), n and beta, with beta varying with n. Set gamma = lim(n ->infinity) n/p1 and sigma = lim(n ->infinity) p1/p2. Suppose that lim(n ->infinity) log n/beta n = 0 and 0 <= sigma gamma < 1. We offer the large deviation for p1+p2/p1 max(1 <= i <= n) lambda i when gamma > 0 via the large deviation of the corresponding empirical measure and via a direct estimate, respectively, when gamma = 0

Automated summary

This paper investigates the properties of beta-Jacobi ensembles under certain conditions. It provides the large deviation of p1+p2/p1 max(1 <= i <= n) lambda i when gamma > 0, and the large deviation of the corresponding empirical measure and a direct estimate when gamma = 0.