Number-Rigidity and β-Circular Riesz gas

31.05.2023, 10:00  –  Campus Golm, Haus 9, Raum 0.17 (and Online)
Forschungsseminar Wahrscheinlichkeitstheorie

David Dereudre (Univ. Lille)

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)=∥x∥^(−s). We focus on the non integrable case d−1<s<d. Our main result ensures, for any dimension d≥1 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 non number rigidity is proved for a Gibbs point process interacting via a non integrable potential. We follow a statistical physics approach based on the canonical DLR equations. It is inspired by Dereudre-Hardy-Leblé-Maïda (2021) where the authors prove the number-rigidity of the Sine β process.

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