{
  "abstract": "In this paper we obtain the critical probability $p_c(Q_{n},r)$ for bootstrap percolation with the infection threshold $r=f(n)n^a$ on the $n$-dimensional hypercube $Q_{n}$, where $0<a<1$ and $f(n)=n^{o(1)}$. More precisely, we obtain the exact first-order and second-order terms of $p_c(Q_{n},r)$ by extending the main theorem of Balogh, Bollob{á}s, and Morris (2009).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26615",
  "author_total": 1,
  "authors": [
    {
      "name": "Fengxing Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83j578tn82mfw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26615",
  "fulltext_url": null,
  "id": "83j578tn82mfw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26615",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223010780",
  "pdf_url": "https://arxiv.org/pdf/2610.26615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83j578tn82mfw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Bootstrap percolation on the hypercube",
  "title_text": "Bootstrap percolation on the hypercube",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/83j578tn82mfw",
  "venue": "arXiv",
  "versions": []
}