Nonstandard limit theorems and large deviation for beta -Jacobi ensembles with a different scaling

Abstract

We consider $\beta$-Jacobi ensembles with parameters $p_1,p_2\ge n.$ We prove that the empirical measure of the rescaled Jacobi ensembles converges weakly to a modified Watcher law via the spectral measure method, which revisits the weak limits obtained in \cite{MaLDPJ} while replacing the condition $\beta n>>\log n$ by $\beta n>>1.$ We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.

23 pages