{
  "abstract": "Suppose $M$ is a planar map with a macroscopic boundary decorated by a spanning tree $T$, such that $(M,T)$ has been sampled from the critical Boltzman measure. We show that $M$ converges to a Liouville quantum gravity disk with parameter $γ=\\sqrt{2}$ under the Tutte embedding as the length of the boundary of $M$ goes to infinity. Furthermore, conditioned on $(M,T)$, the simple random walk on $M$ converges to a planar Brownian motion modulo reparametrization of time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10501",
  "author_total": 1,
  "authors": [
    {
      "name": "Nina Holden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fdrj0xtw8v57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10501",
  "fulltext_url": null,
  "id": "8fdrj0xtw8v57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10501",
  "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.CV"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220971231",
  "pdf_url": "https://arxiv.org/pdf/2610.10501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fdrj0xtw8v57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity",
  "title_text": "The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/8fdrj0xtw8v57",
  "venue": "arXiv",
  "versions": []
}