{
  "abstract": "We prove that flat Jackiw--Teitelboim (JT) gravity arises as a conformal scaling limit of random flat combinatorial disks. We give a clean criterion, formulated in terms of branching explorations, for a discrete model to converge to this conjecturally universal limit. For simplicity, we apply this criterion to a Boltzmann ensemble of disks with rectilinear boundary, defined by summing over combinatorial types and integrating over lengths. As the length of a distinguished side tends to infinity, the rescaled surface converges in law to a continuum random surface prescribed by Ferrari's path-integral formulation of JT gravity. Convergence is in the topology of smooth convergence of the conformal factors on compact subsets of the interior when uniformizing in a fixed domain; the limiting conformal factor is described by a harmonic Gaussian field closely related to holomorphic multiplicative chaos. The crux is a branching exploration of flat JT gravity whose lengths evolve as conditioned Cauchy processes and whose unexplored components are conditionally independent. We construct this exploration using a conformal welding theorem proved in a companion paper, and show that it is the scaling limit of Budd's row-by-row exploration of the discrete disks, analogous to the peeling of random planar maps. Under a tightness condition, our criterion upgrades this convergence to a conformal scaling limit for the discrete disks. Other natural combinatorial disk models admit analogous first-row recursions, providing a route to their scaling limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40645",
  "author_total": 1,
  "authors": [
    {
      "name": "Morris Ang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1x4rgchp2pq6e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40645",
  "fulltext_url": null,
  "id": "1x4rgchp2pq6e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40645",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40645",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1x4rgchp2pq6e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40645",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40645"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "JT gravity as a conformal scaling limit of random flat combinatorial disks",
  "title_text": "JT gravity as a conformal scaling limit of random flat combinatorial disks",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/1x4rgchp2pq6e",
  "venue": "arXiv",
  "versions": []
}