论文标题
戴森模型无标记动力学在无限维
Ergodicity of unlabeled dynamics of Dyson's model in infinite dimensions
论文作者
论文摘要
戴森（Dyson）在无限尺寸中的模型是一个布朗颗粒的系统，它们通过对数电势相互作用，反向温度为$β= 2 $。随机过程可以通过对无限多维随机微分方程的解决方案表示。相关的未标记动力学（扩散过程）由Dirichlet形式以正弦$ _2 $点过程作为参考度量给出。在先前的研究中，我们证明了戴森在无限维度上的模型是不可还原的，但是将未标记动力学的奇特性视为一个开放的问题。在本文中，我们证明了戴森模型在无限维度中的未标记动力学是千古的。
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$. The stochastic process can be represented by the solution to an infinite-dimensional stochastic differential equation. The associated unlabeled dynamics (diffusion process) are given by the Dirichlet form with the sine$ _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.
