Nonstandard Limit Theorems and Large Deviation for β-Jacobi Ensembles with a Different Scaling

Abstract

We consider β-Jacobi ensembles with parameters p₁, p₂ ≥ n. We prove that the empirical measure of the rescaled β-Jacobi ensembles converges weakly to a modified Wachter law via the spectral measure method. We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.