Dyson's model in infinite dimensions is irreducible
Probability
2022-01-03 v2 Mathematical Physics
math.MP
Abstract
Dyson's model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of . The stochastic process is given as a solution to an infinite-dimensional stochastic differential equation. Additionally, a Dirichlet form with the sine point process as a reference measure constructs the stochastic process as a functional of the associated configuration-valued diffusion process. In this paper, we prove that Dyson's model in infinite dimensions is irreducible.
Keywords
Cite
@article{arxiv.2107.10775,
title = {Dyson's model in infinite dimensions is irreducible},
author = {Hirofumi Osada and Ryosuke Tsuboi},
journal= {arXiv preprint arXiv:2107.10775},
year = {2022}
}
Comments
19 pages. To appear in the Festschrift in honor of Professor Fukushima