{
  "abstract": "We prove a good large deviation principle for the scaled unit-area Liouville field on the sphere, in the positive curvature regime and assuming the strict Troyanov condition. The rate function is the renormalized classical Liouville action minus its minimum. Consequently, the field concentrates exponentially at the unique unit-area metric of constant positive curvature with the prescribed conical singularities. The proof combines a joint field-mass large deviation principle with moment bounds that control the positive GMC tilt imposing unit area. This resolves the positive-curvature semiclassical conjecture of Lacoin, Rhodes, and Vargas in this regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Yuchen Fan"
    },
    {
      "name": "Zhenfeng Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91qzbxjbax8qz.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "91qzbxjbax8qz",
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  "landing_url": "https://hal.science/hal-05838591v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-mp"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05838591/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91qzbxjbax8qz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05838591",
      "source": "hal",
      "url": "https://hal.science/hal-05838591v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "The positive-curvature semiclassical limit",
  "title_text": "The positive-curvature semiclassical limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/91qzbxjbax8qz",
  "venue": "HAL",
  "versions": []
}