{
  "abstract": "We prove that in the disk, sphere, whole-plane topology, spanning tree weighted planar maps converge to $\\sqrt{2}$-Liouville quantum gravity disk, sphere or cone under circle packing and Riemann uniformization embedding as the number of faces of the map goes to infinity. As a byproduct, we also prove that the natural path on faces of the embedded tree-weighted planar maps converge to SLE$_8$. The proof is based on our earlier work on circle packing and Riemann uniformization embedding for random planar maps in ergodic scale-free environments, comparisons of circle packings in different domains in a companion paper, and the convergence of tree-weighted planar maps to $\\sqrt{2}$-LQG by the first author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10505",
  "author_total": 2,
  "authors": [
    {
      "name": "Nina Holden"
    },
    {
      "name": "Pu Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1trn4mqhh5c6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10505",
  "fulltext_url": null,
  "id": "c1trn4mqhh5c6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10505",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220992121",
  "pdf_url": "https://arxiv.org/pdf/2610.10505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1trn4mqhh5c6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The circle packing and Riemann uniformization embedding of the tree-weighted planar maps converges to Liouville quantum gravity",
  "title_text": "The circle packing and Riemann uniformization embedding of the tree-weighted planar maps converges to Liouville quantum gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/c1trn4mqhh5c6",
  "venue": "arXiv",
  "versions": []
}