The Infinite Dyson Brownian Motion with $\beta=2$ Does Not Have a Spectral Gap

TL;DR

This paper proves that the Dirichlet forms for the unlabelled infinite Dyson Brownian motion at inverse temperature 2 lack a spectral gap, indicating certain spectral properties of this stochastic process.

Contribution

It establishes the non-existence of a spectral gap for the Dirichlet forms of the infinite Dyson Brownian motion at , a significant theoretical result in stochastic analysis.

Findings

No spectral gap for the Dirichlet forms at 

Implications for the spectral properties of Dyson Brownian motion

Advances understanding of infinite-dimensional stochastic processes

Abstract

We prove that the Dirichlet forms associated with the unlabelled infinite Dyson Brownian motion with the inverse temperature $\beta=2$ do not have a spectral gap.