{
  "abstract": "We prove that, for all $β>0$, the Dobrushin-Lanford-Ruelle (DLR) equations for the unit-intensity $\\mathsf{Sine}_β$ 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 $\\mathsf{Sine}_β$. 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06832",
  "author_total": 1,
  "authors": [
    {
      "name": "Theodoros Assiotis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zjqcxg7aeg54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06832",
  "fulltext_url": null,
  "id": "7zjqcxg7aeg54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06832",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7211997884",
  "pdf_url": "https://arxiv.org/pdf/2609.06832",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zjqcxg7aeg54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06832",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06832"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniqueness for DLR equations of $\\mathsf{Sine}_β$",
  "title_text": "Uniqueness for DLR equations of Sine_β",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/7zjqcxg7aeg54",
  "venue": "arXiv",
  "versions": []
}