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arXiv · 2609.06832

Uniqueness for DLR equations of $\mathsf{Sine}_\beta$

Theodoros Assiotis
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Abstract

We prove that, for all $\beta>0$, the Dobrushin-Lanford-Ruelle (DLR) equations for the unit-intensity $\mathsf{Sine}_\beta$ point process have a unique stationary solution under a particular finite electric energy condition. Uniqueness fails if this condition is dropped. This answers a question of Dereudre-Hardy-Lebl\'e-Ma\"ida and gives a canonical statistical physics characterisation of $\mathsf{Sine}_\beta$. The main technical ingredient is a relative entropy estimate which allows us to compare the conditional distribution in a finite box of a DLR solution to a corresponding circular $\beta$ ensemble.

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Theodoros Assiotis. 2026-09-06. Uniqueness for DLR equations of $\mathsf{Sine}_\beta$. https://arxiv.org/abs/2609.06832

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