{
  "abstract": "In this paper we construct a one-parameter family of periodic Airy line ensembles $\\mathcal{A}^{\\mathrm{per},R}$ for $R>0$ as weak scaling limits of Borodin's periodic Schur processes. We establish several properties of $\\mathcal{A}^{\\mathrm{per},R}$, including a determinantal point process structure with an explicit correlation kernel. We also show that, after a parabolic shift and normalization, $\\mathcal{A}^{\\mathrm{per},R}$ satisfies, on its domain $[-R/2,R/2]$, the same Brownian Gibbs property enjoyed by the usual Airy line ensemble. A main technical contribution of the paper is a general tightness criterion for determinantal line ensembles, which extends the argument used by Johansson in [Comm. Math. Phys. 242 (2003), 277-329] to prove a functional limit theorem for the discrete polynuclear growth model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16611",
  "author_total": 4,
  "authors": [
    {
      "name": "Evgeni Dimitrov"
    },
    {
      "name": "Samir Sarieddine"
    },
    {
      "name": "Zongrui Yang"
    },
    {
      "name": "Zhengye Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bqq7n88b72edb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16611",
  "fulltext_url": null,
  "id": "bqq7n88b72edb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16611",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
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    [
      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7221776224",
  "pdf_url": "https://arxiv.org/pdf/2610.16611",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqq7n88b72edb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16611",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16611"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The periodic Airy line ensembles",
  "title_text": "The periodic Airy line ensembles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bqq7n88b72edb",
  "venue": "arXiv",
  "versions": []
}