{
  "abstract": "We show that, for any infinite transitive graph $G$, the infinite cluster after supercritical percolation almost surely inherits the anchored isoperimetry of $G$. Moreover, the probability of violating the corresponding isoperimetric inequality decays exponentially in the isoperimetric profile of the host graph. This was previously known only for nonamenable transitive graphs, $\\mathbb{Z}^d$, and very recently for transitive graphs of polynomial growth. Our proof combines the thinning-and-sprinkling technique with a novel counting algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38941",
  "author_total": 5,
  "authors": [
    {
      "name": "Sahar Diskin"
    },
    {
      "name": "Lyuben Lichev"
    },
    {
      "name": "Ritvik Ramanan Radhakrishnan"
    },
    {
      "name": "Benny Sudakov"
    },
    {
      "name": "Laury Verhoeven"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vn6yctt2h9g3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38941",
  "fulltext_url": null,
  "id": "1vn6yctt2h9g3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38941",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vn6yctt2h9g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Anchored isoperimetry in percolation",
  "title_text": "Anchored isoperimetry in percolation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1vn6yctt2h9g3",
  "venue": "arXiv",
  "versions": []
}