On the ergodicity of interacting particle systems under number rigidity

被引:1
|
作者
Suzuki, Kohei [1 ]
机构
[1] Univ Durham, Dept Math Sci, South Rd, Durham DH1 3LE, England
关键词
Ergodicity; Tail triviality; Optimal transport; Number rigidity; DETERMINANTAL POINT-PROCESSES; DIFFUSION-PROCESSES; CONFIGURATION-SPACES; LARGE DEVIATIONS; DIRICHLET FORMS; BROWNIAN-MOTION; CONSTRUCTION; EQUATIONS; GEOMETRY;
D O I
10.1007/s00440-023-01243-3
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure mu on the configuration space Gamma; (b) the finiteness of a suitable L-2-transportation-type distance (d) over bar (Gamma); (c) the irreducibility of local mu-symmetric Dirichlet forms on Gamma. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including sine(2), Airy(2), Bessel(alpha,2) (alpha >= 1), and Ginibre point processes. In particular, the case of the 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.
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页码:583 / 623
页数:41
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