{
  "abstract": "We investigate the restoration of isotropy for anisotropic diffusions on pre-Sierpiński carpets in the plane, a problem previously studied by Barlow, Hattori, Hattori and Watanabe \\cite{BHHW} in which they obtained a weak homogenization property for the ratio of effective resistances of the anisotropic diffusions. We establish the weak convergence of these anisotropic diffusions to Brownian motion on the Sierpiński carpet. As a consequence, we give an affirmative answer to the strong homogenization conjecture raised in \\cite[p.3]{BHHW}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04936",
  "author_total": 3,
  "authors": [
    {
      "name": "Shiping Cao"
    },
    {
      "name": "Zhen-Qing Chen"
    },
    {
      "name": "Hua Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg13cb016zt7p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04936",
  "fulltext_url": null,
  "id": "eg13cb016zt7p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04936",
  "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": "W7211892903",
  "pdf_url": "https://arxiv.org/pdf/2609.04936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eg13cb016zt7p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04936"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Homogenization of anisotropic diffusion on pre-Sierpiński carpets",
  "title_text": "Homogenization of anisotropic diffusion on pre-Sierpiński carpets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/eg13cb016zt7p",
  "venue": "arXiv",
  "versions": []
}