On the ergodicity of interacting particle systems under number rigidity

Suzuki, Kohei

doi:10.1007/s00440-023-01243-3

On the ergodicity of interacting particle systems under number rigidity

Suzuki, Kohei

Authors

Dr Kohei Suzuki kohei.suzuki@durham.ac.uk
Assistant Professor

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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