Ergodicity of unlabeled dynamics of Dyson’s model in infinite dimensions
Ergodicity of unlabeled dynamics of Dyson’s model in infinite dimensions
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DOI：
10.1063/5.0086873
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发表时间：
2022-03
影响因子：
1.3
通讯作者：
H. Osada;Shota Osada
中科院分区：
文献类型：
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作者：
H. Osada;Shota Osada
无限维的戴森模型是一个布朗粒子系统，它们通过对数势相互作用，温度的倒数为β = 2。随机过程可以用无穷维随机微分方程的解来表示。相关的未标记动力学（扩散过程）由Dirichlet形式给出，其中sine2点过程作为参考测度。在以前的研究中，我们证明了戴森模型在无限维是不可约的，但留下的遍历性的未标记的动力学作为一个开放的问题。本文证明了无限维Dyson模型的未标号动力学是遍历的。
Dyson’s model in infinite dimensions is a system of Brownian particles that interact via a logarithmic potential with an inverse temperature of β = 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 sine2 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.