{
  "abstract": "Let $M$ be a closed connected Riemannian manifold. A continuous semimartingale segment can be closed by a Borel family of paths of uniformly bounded length, producing a singular homology class $H_t\\in H_1(M;\\R)$. For every linear choice of smooth closed representatives of $H^1(M;\\R)$, the corresponding Stratonovich homology differs from $H_t$ by a uniformly bounded term, almost surely and uniformly in time. The classes $H_t$ are additive under time shift up to a uniformly bounded error. For Brownian motion this comparison yields the Gaussian central limit theorem with covariance given by the normalized Hodge inner product, a functional central limit theorem for the polygonal interpolation of the closed homology classes, and the almost sure limit $H_t/t\\to0$. For elliptic diffusions, the large-deviation principle of Galkin--Mariani passes to $H_T/T$ with the same rate function. The construction uses Schwartzman's closing procedure and is independent, at these asymptotic scales, of the chosen bounded closing family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27851",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto Verjovsky"
    },
    {
      "name": "Ricardo F. Vila-Freyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dkgppy1564n0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27851",
  "fulltext_url": null,
  "id": "1dkgppy1564n0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27851",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214185315",
  "pdf_url": "https://arxiv.org/pdf/2609.27851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dkgppy1564n0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Brownian Loops, Singular Homology, and Asymptotic Cycles",
  "title_text": "Brownian Loops, Singular Homology, and Asymptotic Cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1dkgppy1564n0",
  "venue": "arXiv",
  "versions": []
}