{
  "abstract": "We give an estimate for the distribution tail of the passage time between $0$ and $\\infty$ in first-passage percolation on $\\mathbb Z^d$, when the weight distribution is bounded and has a supercritical atom at $0$. A special case involves the number of disjoint cutsets between $0$ and $\\infty$ in supercritical bond percolation. Besides, we show that the rate function for the upper-tail deviations of the point-to-point passage time is asymptotically polynomial near $0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18033",
  "author_total": 1,
  "authors": [
    {
      "name": "Julien Verges"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbeeeyt60rsf7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18033",
  "fulltext_url": null,
  "id": "dbeeeyt60rsf7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18033",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221798659",
  "pdf_url": "https://arxiv.org/pdf/2610.18033",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbeeeyt60rsf7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18033",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18033"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Distribution tail of the distance to infinity in supercritical bond percolation",
  "title_text": "Distribution tail of the distance to infinity in supercritical bond percolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/dbeeeyt60rsf7",
  "venue": "arXiv",
  "versions": []
}