The stochastic Bessel operator at high temperatures

TL;DR

This paper investigates the high-temperature behavior of the stochastic Bessel operator's eigenvalues, showing their convergence to a limiting process described by coupled stochastic differential equations, extending understanding of spectral limits in random matrix theory.

Contribution

It introduces a new high-temperature limit analysis for the stochastic Bessel operator's eigenvalues, revealing their convergence to a novel limiting point process.

Findings

Eigenvalues' point process converges to a new limiting process

Coupled stochastic differential equations characterize the limit

Extends spectral analysis in high-temperature regimes

Abstract

We know from Ram{\'i}rez and Rider that the hard edge of the spectrum of the Beta-Laguerre ensemble converges, in the high-dimensional limit, to the bottom of the spectrum of the stochastic Bessel operator. Using stochastic analysis techniques, we show that, in the high temperatures limit, the rescaled eigenvalues point process of the stochastic Bessel operator converges to a limiting point process characterized with coupled stochastic dierential equations.