On the Ergodicity of Interacting Particle Systems under Number Rigidity

2022/03/29 by Suzuki, Kohei · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2203.15750

Abstract

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 L²-transportation-type distance \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 sine₂, Airy₂, Bessel_{α, 2} (α≥ 1), and 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.

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