Ergodicity of unlabeled dynamics of Dyson's model in infinite dimensions

Abstract

Dyson's model in infinite dimensions is a system of Brownian particles that interact via a logarithmic potential with an inverse temperature of $\beta =2$. The stochastic process can be represented by the solution to an infinite-dimensional stochastic differential equation. The associated unlabeled dynamics (diffusion process) are given by the Dirichlet form with the sine${}_2$ point process as a reference measure. In a previous study, we proved that Dyson's model in infinite dimensions is irreducible, but left the ergodicity of the unlabeled dynamics as an open problem. In this paper, we prove that the unlabeled dynamics of Dyson's model in infinite dimensions are ergodic.

arXiv comment16 pages. arXiv admin note: text overlap with arXiv:2107.10775

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Cited by in corpus (2)

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