Beta Jacobi processes

TL;DR

This paper introduces a multidimensional process that extends matrix Jacobi eigenvalue processes and whose stationary distribution aligns with the beta Jacobi ensemble, providing a new framework for understanding these distributions.

Contribution

It defines and analyzes a novel multidimensional process that generalizes eigenvalues of matrix Jacobi processes and connects to the beta Jacobi ensemble.

Findings

The process's stationary distribution matches the beta Jacobi ensemble.

The process generalizes classical matrix Jacobi eigenvalue processes.

Provides new insights into the structure of beta Jacobi distributions.

Abstract

We define and study a multidimensional process that generalizes the eigenvalues of matrix Jacobi processes on the one hand and whose stationary distribution is given by the beta Jacobi ensemble on the other hand.