{
  "abstract": "We study inference on the strength of Gaussian multiplicative chaos from one geometric graph with unobserved vertex positions. In the planar model, the edge-count statistic has a piecewise deterministic limit with a transition at $γ=1$, whereas degree quantiles consistently estimate $ν=γ^2/2$ throughout the subcritical range. Fractional moments give uniform finite-sample risk bounds. At finite resolution, common graph envelopes calibrate tests over continuous parameter boxes with unknown Poisson intensity. They give simultaneous coverage under adaptive refinement for a fixed statistic, and conditional coverage for an independently piloted size--degree residual on a fixed partition. For the exact periodic FFT--pixel approximation, we prove explicit total-variation rates for the annealed spatial Cox law and the observed graph law, uniformly on every compact subcritical range $0\\leγ\\leΓ<2$. The rates allow intensity to grow with resolution and imply uniform asymptotic coverage after recalibration at each resolution. Numerical studies examine parameter refinement, residual calibration, and multiresolution stability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11597",
  "author_total": 1,
  "authors": [
    {
      "name": "Chunhao Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72e2c2tysb3k4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11597",
  "fulltext_url": null,
  "id": "72e2c2tysb3k4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11597",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221184608",
  "pdf_url": "https://arxiv.org/pdf/2610.11597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72e2c2tysb3k4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Single-graph inference for fractal Gaussian networks",
  "title_text": "Single-graph inference for fractal Gaussian networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/72e2c2tysb3k4",
  "venue": "arXiv",
  "versions": []
}