{
  "abstract": "In this article, we study the spatial fluctuations of the Skorohod solution to a stochastic heat equation on $\\mathbb R^d$ for $d<4$, driven by multiplicative Gaussian noise with the non-separable covariance kernel $p_{|t-s|}(x-y)$. We prove that the solution is strictly stationary and spatially ergodic at every fixed time. For the centered spatial integral $F_R(t)=\\int_{\\{|x|<R\\}}(u(t,x)-1)dx,$ we show that $\\mathbb E[F_R(t)F_R(s)]\\sim K(t,s)R^d$ as $R\\to\\infty$. Using moment estimates for the first two Malliavin derivatives and a second-order Gaussian Poincaré inequality, we establish a quantitative central limit theorem in total variation distance with rate $R^{-d/2}$. We also prove a functional central limit theorem for the process $\\{R^{-d/2}F_R(t)\\}_{t\\geq0}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04941",
  "author_total": 2,
  "authors": [
    {
      "name": "Meng Wang"
    },
    {
      "name": "Wangjun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bsw271112pws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04941",
  "fulltext_url": null,
  "id": "8bsw271112pws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04941",
  "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": "W7220649795",
  "pdf_url": "https://arxiv.org/pdf/2610.04941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bsw271112pws.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Central limit theorems for stochastic heat equation driven by Gaussian noise with heat-kernel covariance",
  "title_text": "Central limit theorems for stochastic heat equation driven by Gaussian noise with heat-kernel covariance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8bsw271112pws",
  "venue": "arXiv",
  "versions": []
}