{
  "abstract": "We consider long-range percolation (LRP) on $\\mathbb{Z}^d, d \\ge 1$ with connection probabilities $\\mathbf{p}(x, y) \\approx \\fracβ{\\|x-y\\|^s}$ for $β>0$ and $s > \\min(2d, d+2)$. Our main result is that the mixing time of the random walk on the giant component of supercritical LRP inside a box of side length $n$ is of order $n^2$. To establish the upper bound, we show that a $d$-dimensional isoperimetric inequality holds almost surely simultaneously for all connected sets inside the giant component that are large enough.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11808",
  "author_total": 2,
  "authors": [
    {
      "name": "Dieter Mitsche"
    },
    {
      "name": "Carlo Scali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qfr9ca8kseyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11808",
  "fulltext_url": null,
  "id": "6qfr9ca8kseyh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11808",
  "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": "W7221177151",
  "pdf_url": "https://arxiv.org/pdf/2610.11808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qfr9ca8kseyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Mixing time and isoperimetry of long-range percolation in the diffusive regime",
  "title_text": "Mixing time and isoperimetry of long-range percolation in the diffusive regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6qfr9ca8kseyh",
  "venue": "arXiv",
  "versions": []
}