论文标题
关于在数字刚度下相互作用的粒子系统的登山性
On the Ergodicity of Interacting Particle Systems under Number Rigidity
论文作者
论文摘要
在本文中，我们提供以下属性之间的关系：（a）在配置空间上$ {\boldsymbolυ} $上的概率度量$μ$的尾巴微不足道； （b）$ l^2 $ -transportation-type距离$ \ bar {\ mathsf d} _ {\boldsymbolυ} $的有限性; （c）$ {\boldsymbolυ} $上的$μ$ - 符合dirichlet的不可约性。作为一种应用，我们获得了具有对数/永久点过程的对数相互作用的相互作用的无限相互作用的相互作用无限扩散（包括$ \ mathrm {sine} _ {2} $，$ \ mathrm {airy {airy} $ { $ \ mathrm {bessel} _ {α，2} $（$α\ ge 1 $）和$ \ mathrm {ginibre} $ point Processes，尤其是未标记的Dyson Brownian Motion的情况。为了证明，从戈什（Ghosh）意义上讲，点过程的数量刚度 - peres起着关键作用。
In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure $μ$ on the configuration space ${\boldsymbolΥ}$; (b) the finiteness of the $L^2$-transportation-type distance $\bar{\mathsf d}_{\boldsymbolΥ}$; (c) the irreducibility of $μ$-symmetric Dirichlet forms on ${\boldsymbolΥ}$. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction arisen from determinantal/permanental point processes including $\mathrm{sine}_{2}$, $\mathrm{Airy}_{2}$, $\mathrm{Bessel}_{α, 2}$ ($α\ge 1$), and $\mathrm{Ginibre}$ point processes, in particular, the case of unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh--Peres plays a key role.
