NUMBER-RIGIDITY AND β-CIRCULAR RIESZ GAS

• 成果类型: Article
• 署名作者: Dereudre, David; Vasseur, Thibaut
• 署名单位: Universite de Lille; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1606
• 发表日期: 2023
• 页码: 1025-1065
• 关键词: principle; EQUATIONS; log

摘要

For an inverse temperature /3 > 0, we define the /3-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = IlxII-s. We focus on the nonintegrable case d -1 < s < d. Our main result ensures, for any dimension d > 1 and inverse temperature /3 > 0, the existence of a /3-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 A is a function of the point configuration outside Delta. 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 Sine/3 process.