{
  "abstract": "We study bidirected percolation on an undirected graph $G$: each edge is replaced by two oppositely directed edges, each of which is open independently with probability $p$. Two vertices are strongly connected if they are mutually reachable by open directed paths. Let $p_\\mathrm{sc}$ denote the threshold for the existence of an infinite strongly connected cluster, and let $p_c$ denote the usual Bernoulli percolation threshold on $G$. On every transitive amenable graph, we prove that $p_\\mathrm{sc}=p_c$. In contrast, sufficiently spread-out modifications of every transitive non-amenable graph satisfy $p_\\mathrm{sc}>p_c$. We also show that, on $\\mathbb Z^d$ with $d\\ge11$, the expected size of the strongly connected cluster is finite at $p=p_\\mathrm{sc}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28762",
  "author_total": 3,
  "authors": [
    {
      "name": "Yucheng Liu"
    },
    {
      "name": "Leonardo T. Rolla"
    },
    {
      "name": "Yuliang Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arqga46nv5412.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28762",
  "fulltext_url": null,
  "id": "arqga46nv5412",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28762",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223240930",
  "pdf_url": "https://arxiv.org/pdf/2610.28762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arqga46nv5412.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.28762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Percolation on Bidirected Graphs",
  "title_text": "Percolation on Bidirected Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/arqga46nv5412",
  "venue": "arXiv",
  "versions": []
}