{
  "abstract": "For a class of smooth stationary Gaussian fields, we study the fluctuations of the volume, surface area and Euler characteristic of the unbounded excursion component in growing boxes $Λ_n=[-n,n]^d$. We establish nondegenerate central limit theorems for all three functionals throughout the supercritical regime in every dimension $d\\geq 2$. We further quantify these central limit theorems by establishing Berry--Esseen bounds of order $O\\bigl(|Λ_n|^{-(1-1/s)}\\bigr)$ in Kolmogorov distance, where $s\\in(1,2]$ depend on the regularity and decay assumptions. Especially for the Bargmann--Fock field, we obtain a Berry--Esseen bound of $O\\bigl(|Λ_n|^{-1/2}\\bigr)$ for all three functionals. A matching lower bound shows that this rate is sharp for the Euler characteristic. For the volume, we improve the previously known rate of $O\\bigl(|Λ_n|^{-1/2}(\\log|Λ_n|)^{2d}\\bigr)$. We mainly use Stein's method and moment bounds for differences arising from white-noise resampling to finish our proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37240",
  "author_total": 4,
  "authors": [
    {
      "name": "Yu Cheng"
    },
    {
      "name": "Song-Hao Liu"
    },
    {
      "name": "Qi-Man Shao"
    },
    {
      "name": "Jing-Yu Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fy5t2mg50a7d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37240",
  "fulltext_url": null,
  "id": "1fy5t2mg50a7d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37240",
  "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"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7224127925",
  "pdf_url": "https://arxiv.org/pdf/2610.37240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fy5t2mg50a7d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Three quantitative central limit theorems for the unbounded excursion component of a Gaussian field",
  "title_text": "Three quantitative central limit theorems for the unbounded excursion component of a Gaussian field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1fy5t2mg50a7d",
  "venue": "arXiv",
  "versions": []
}