{
  "abstract": "In this paper, we prove that the uniform spanning tree of $\\mathbb Z^4$, seen from the origin, converges locally to an infinite spatial Brownian Kesten tree: a Brownian spine onto which independent spatial Brownian trees are grafted at a constant rate. The convergence holds jointly for the intrinsic metric, the volume measure and the Euclidean positions of the vertices, after rescaling these quantities by suitable constant multiples of $n^{-1}$, $n^{-2}(\\log n)^{1/3}$ and $n^{-1/2}(\\log n)^{-1/6}$, respectively, under the local rooted spatial Gromov-weak topology. The rescaled space-time occupation measure converges to that of infinite canonical super-Brownian motion. We also identify the limiting law of the rescaled intrinsic-ball volume and obtain sharp first-moment asymptotics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03582",
  "author_total": 1,
  "authors": [
    {
      "name": "Runsheng Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5b7p00hb79wmr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03582",
  "fulltext_url": null,
  "id": "5b7p00hb79wmr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03582",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03582",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5b7p00hb79wmr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03582",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03582"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Local scaling limit of the four-dimensional uniform spanning tree",
  "title_text": "Local scaling limit of the four-dimensional uniform spanning tree",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/5b7p00hb79wmr",
  "venue": "arXiv",
  "versions": []
}