{
  "abstract": "Fix $W\\in(0,2)$ and let $γ\\downarrow0$. We prove that a weight-$W$ quantum disk conditioned to have unit quantum area converges, in the maximum-embedded strip, to the deterministic field $ϕ_W(t+iθ)=\\log(W/(4π))-2\\log\\cosh(Wt/2)$ and its constant-curvature area measure. The proof establishes a joint large-deviation principle for the radial Brownian input, the lateral Gaussian free field, and the total Gaussian multiplicative chaos mass. Diverging-order moment bounds justify both adjoining the noncontinuous area functional and retaining its unbounded positive power in the unit-area expectation. An exact radial Girsanov shift centers the candidate, and reflection together with the sharp Onofri inequality proves its unique optimality. This yields concentration without a quadratic expansion of the running maximum or an order-one partition-function asymptotic. We also identify the field rate with the renormalized Liouville action in the maximum embedding.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02436",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuchen Fan"
    },
    {
      "name": "Zhenfeng Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvk4xjkw9782v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02436",
  "fulltext_url": null,
  "id": "fvk4xjkw9782v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02436",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220358087",
  "pdf_url": "https://arxiv.org/pdf/2610.02436",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvk4xjkw9782v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02436",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02436"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The semiclassical limit of unit-area quantum disks",
  "title_text": "The semiclassical limit of unit-area quantum disks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/fvk4xjkw9782v",
  "venue": "arXiv",
  "versions": []
}