PreprintCC BY 4.0arXiv
Uniqueness for DLR equations of Sineβ
Abstract
We prove that, for all β>0, the Dobrushin-Lanford-Ruelle (DLR) equations for the unit-intensity Sineβ 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-Leblé-Maïda and gives a canonical statistical physics characterisation of Sineβ. 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 β ensemble.
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BibTeX
@misc{assiotis2026uniqueness,
title = {{Uniqueness for DLR equations of $\mathsfSine_β$}},
author = {Theodoros Assiotis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06832},
eprint = {2609.06832},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06832},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniqueness for DLR equations of Sine_β
AU - Theodoros Assiotis
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06832
UR - https://arxiv.org/abs/2609.06832
AB - We prove that, for all β>0, the Dobrushin-Lanford-Ruelle (DLR) equations for the unit-intensity Sine_β 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-Leblé-Maïda and gives a canonical statistical physics characterisation of Sine_β. 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 β ensemble.
ER -