Edge scaling of the \beta-Jacobi ensemble

TL;DR

This paper investigates the spectral edge behavior of the eta-Jacobi ensemble, demonstrating that its scaling limits align with the stochastic Airy and Bessel processes for various eta values.

Contribution

It establishes the connection between the eta-Jacobi ensemble's edge scaling limits and known stochastic point processes for general eta.

Findings

Limiting processes at soft and hard edges identified as stochastic Airy and Bessel processes.

Results hold for general eta values.

Provides a unified framework for understanding spectral edge behavior.

Abstract

We study the scaling limit of the spectrum of the \beta-Jacobi ensemble at the soft-edge and hard-edge for general values of \beta. 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.