{
  "abstract": "In this article, we consider the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data. We prove a functional central limit theorem for the spatial average of the solution, which solves an open problem from Gu and Pu (2025). Our main tool is Clark-Ocone formula from Malliavin calculus, combined with an in-depth analysis of the increments of the solution. The main step is a moment bound for time increments of the normalized spatial integral. For this, we introduce a new technique, called a ``common-ray'' change of variables. Using the fact that Malliavin derivative of the solution satisfies a Chapman-Kolmogorov relation, we reduce the kernel differences at two times to spatial increments at one common time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27219",
  "author_total": 3,
  "authors": [
    {
      "name": "Raluca M. Balan"
    },
    {
      "name": "Le Chen"
    },
    {
      "name": "Jinxin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/077nxz2fg9c4q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27219",
  "fulltext_url": null,
  "id": "077nxz2fg9c4q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27219",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223147551",
  "pdf_url": "https://arxiv.org/pdf/2610.27219",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/077nxz2fg9c4q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27219",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27219"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A functional central limit theorem for the KPZ equation with narrow wedge initial data",
  "title_text": "A functional central limit theorem for the KPZ equation with narrow wedge initial data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/077nxz2fg9c4q",
  "venue": "arXiv",
  "versions": []
}