{
  "abstract": "In planar soft-stick percolation, each vertex of the square lattice independently opens one uniformly chosen outgoing arrow and, with probability $ε$, the opposite arrow as well. Motivated by the question on its critical parameter raised by Bäumler et al., we prove that $ε_{c}\\le0.99<1$, establishing percolation below the two-arrow endpoint. More precisely, at $ε=0.99$ the origin has an infinite forward cluster with probability greater than 11/20. The proof uses a Peierls argument in which boundary turns are encoded by a three-state transfer matrix to bound the contour sum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10067",
  "author_total": 1,
  "authors": [
    {
      "name": "Shitao Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tbqna1a2bn3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10067",
  "fulltext_url": null,
  "id": "2tbqna1a2bn3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10067",
  "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": "W7212188688",
  "pdf_url": "https://arxiv.org/pdf/2609.10067",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tbqna1a2bn3f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10067",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10067"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Peierls bound for planar soft-stick percolation",
  "title_text": "A Peierls bound for planar soft-stick percolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/2tbqna1a2bn3f",
  "venue": "arXiv",
  "versions": []
}