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On the ergodicity of interacting particle systems under number rigidity

Suzuki, Kohei

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Abstract

In this paper, we provide relations among the following properties: the tail triviality of a probability measure μ on the configuration space Υ; the finiteness of a suitable L2-transportation-type distance d¯Υ; the irreducibility of local μ-symmetric Dirichlet forms on Υ. 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 sine2, Airy2, Besselα, 2 (α≥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.

Citation

Suzuki, K. (2024). On the ergodicity of interacting particle systems under number rigidity. Probability Theory and Related Fields, 188(1-2), 583-623. https://doi.org/10.1007/s00440-023-01243-3

Journal Article Type Article
Acceptance Date Oct 7, 2023
Online Publication Date Dec 2, 2023
Publication Date Feb 1, 2024
Deposit Date Jan 9, 2024
Publicly Available Date Jan 9, 2024
Journal Probability Theory and Related Fields
Print ISSN 0178-8051
Electronic ISSN 1432-2064
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 188
Issue 1-2
Pages 583-623
DOI https://doi.org/10.1007/s00440-023-01243-3
Keywords Number rigidity, 31C25, Tail triviality, 70F45, 60G55, Ergodicity, Optimal transport, 30L99, 37A30
Public URL https://durham-repository.worktribe.com/output/2117458

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