{
  "abstract": "Let \\(\\{Z_n\\}_{n\\geq0}\\) be a supercritical branching random walk with deterministic rooted \\(b\\)-ary tree, \\(b\\geq2\\), and symmetric displacements satisfying \\(\\lim_{x\\to+\\infty}x^{-α}\\log\\Pp(X>x)=-λ\\) with \\(α,λ>0\\). Set $\\overline Z_n(\\cdot):=Z_n(\\cdot)/Z_n(\\mathbb{R}),~n\\geq0.$ For a finite union \\(A\\) of intervals, we establish the following full large-deviation principle: for every Borel set \\(Γ\\subset[0,1]\\), \\begin{align*} -\\inf_{q\\inΓ^\\circ}Q_A(q) &\\leq \\liminf_{n\\to\\infty}n^{-α/2} \\log\\Pp\\!\\left(\\overline Z_n(\\sqrt n\\,A)\\inΓ\\right) &\\leq \\limsup_{n\\to\\infty}n^{-α/2} \\log\\Pp\\!\\left(\\overline Z_n(\\sqrt n\\,A)\\inΓ\\right) &\\leq -\\inf_{q\\in\\overlineΓ}Q_A(q), \\end{align*} where $Q_A$ is a good rate function on $[0,1]$. Meanwhile, we obtain large deviation probabilities for $\\{\\overline Z_n(\\sqrt n\\,A)\\}_{n\\geq1}.$ This strengthens the nonmatching upper and lower bounds obtained by Chen and He [Probab. Theory Related Fields 175 (2019) 255-307] for regular trees with Weibull displacements. Our method combines a large-deviation principle for rescaled displacement tree fields and exponential equivalence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08714",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuxiong Zhang"
    },
    {
      "name": "Yaping Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44zf90j8rzwdb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08714",
  "fulltext_url": null,
  "id": "44zf90j8rzwdb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08714",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212012614",
  "pdf_url": "https://arxiv.org/pdf/2609.08714",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44zf90j8rzwdb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08714",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08714"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A large-deviation principle for the empirical distribution of a regular branching random walk",
  "title_text": "A large-deviation principle for the empirical distribution of a regular branching random walk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/44zf90j8rzwdb",
  "venue": "arXiv",
  "versions": []
}