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Dyson's model in infinite dimensions is irreducible
Hirofumi Osada, Ryosuke Tsuboi · 2021-07-23 · via math.PR updates on arXiv.org

Dyson's model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of $ β= 2$. The stochastic process is given as a solution to an infinite-dimensional stochastic differential equation. Additionally, a Dirichlet form with the sine$ _2$ 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.

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