May 2023 Number-rigidity and β-circular Riesz gas
David Dereudre, Thibaut Vasseur
Author Affiliations +
Ann. Probab. 51(3): 1025-1065 (May 2023). DOI: 10.1214/22-AOP1606


For an inverse temperature β>0, we define the β-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x)=xs. We focus on the nonintegrable case d1<s<d. Our main result ensures, for any dimension d1 and inverse temperature β>0, the existence of a β-circular Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel set Δ is a function of the point configuration outside Δ. It is the first time that the nonnumber-rigidity is proved for a Gibbs point process interacting via a nonintegrable potential. We follow a statistical physics approach based on the canonical DLR equations. It is inspired by the recent paper (Comm. Pure Appl. Math. 74 (2021) 172–222) where the authors prove the number-rigidity of the Sineβ process.


Download Citation

David Dereudre. Thibaut Vasseur. "Number-rigidity and β-circular Riesz gas." Ann. Probab. 51 (3) 1025 - 1065, May 2023.


Received: 1 April 2021; Revised: 1 August 2022; Published: May 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583062
zbMATH: 07690055
Digital Object Identifier: 10.1214/22-AOP1606

Primary: 60G55 , 60K35
Secondary: 82B21

Keywords: DLR equations , equivalence of ensembles , Gibbs point process

Rights: Copyright © 2023 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.51 • No. 3 • May 2023
Back to Top