{
  "abstract": "We consider independent long-range bond percolation on $\\mathbb{Z}^d$ in which $x$ and $y$ are joined with probability $1-e^{-βJ(x-y)}$. Let $d\\ge2$ and let $J$ be invariant under coordinate permutations and sign changes, positive on nearest-neighbour pairs, and satisfy $\\liminf_{n\\to\\infty} n^d\\sum_{\\|x\\|>n}J(x)=0$. We prove that there is no infinite cluster at the critical parameter. Together with Berger's theorem for heavy tails, this gives continuity of the phase transition for $J(x)\\asymp\\|x\\|^{-d-α}$ for every $α>0$ except $α=d$, in every dimension $d\\ge2$, and for every exponentially decaying kernel satisfying these hypotheses. Previously the fast-decaying case was known for nearest-neighbour and uniform finite-range kernels, in $d=2$ for finite-range and exponential kernels, and in high dimension for sufficiently spread-out kernels. The proof adapts a recent renormalization argument for nearest-neighbour percolation on $\\mathbb{Z}^3$ that is driven by a gluing inequality conjectured by Kozma and Nitzan. Long edges enter in two places: they can jump over the surfaces that a nearest-neighbour path must cross, and they let a cluster outside a box enter it from far away. We control the first with thick outer faces and the tail condition, and the second by measuring entrances through the total edge weight between a cluster and a box rather than through the number of boundary vertices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01490",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czcnf7v2n0w9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01490",
  "fulltext_url": null,
  "id": "czcnf7v2n0w9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01490",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czcnf7v2n0w9s.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "No infinite cluster at criticality for long-range percolation with fast-decaying interactions",
  "title_text": "No infinite cluster at criticality for long-range percolation with fast-decaying interactions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/czcnf7v2n0w9s",
  "venue": "arXiv",
  "versions": []
}