Edge scaling of the β-Jacobi ensemble

Abstract

We study the scaling limit of the spectrum of the β-Jacobi ensemble at the soft-edge and hard-edge for general values of β. We show that the limiting point processes correspond respectively to the stochastic Airy and Bessel point processes introduced in Ramirez-Rider-Virag and Ramirez-Rider.

Minor changes

References in corpus (15)

• Level-Spacing Distributions and the Airy Kernel
• Matrix Models for Beta Ensembles
• Level-Spacing Distributions and the Bessel Kernel
• Level-Spacing Distributions and the Airy Kernel
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• Continuum limits of random matrices and the Brownian carousel
• From Random Matrices to Stochastic Operators
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence
• Limits of spiked random matrices I
• Product of random projections, Jacobi ensembles and universality problems arising from free probability
• Diffusion at the random matrix hard edge
• Matrix models for circular ensembles
• Tridiagonal realization of the anti-symmetric Gaussian $\beta$-ensemble
• Limit Theorems for Beta-Jacobi Ensembles
• Some asymptotic properties of the spectrum of the Jacobi ensemble

Cited by in corpus (3)

• Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
• Asymptotics for products of characteristic polynomials in classical $\beta$-Ensembles
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution