{
  "abstract": "We consider Poisson Boolean percolation on Rd with power-law distribution on the radius with a finite d-moment for d≥2. We prove that subcritical sharpness occurs for all but a countable number of power-law distributions. This extends the results of Duminil-Copin–Raoufi–Tassion (Ann. Henri Lebesgue 3 (2020) 677–700) where subcritical sharpness is proved under the assumption that the radii distribution has a 5d−3 finite moment. Our proofs techniques are different from (Ann. Henri Lebesgue 3 (2020) 677–700): we do not use a randomized algorithm and rely on specific independence properties of Boolean percolation, inherited from the underlying Poisson process. We also prove supercritical sharpness for any distribution with a finite d-moment and the continuity of the critical parameter for the truncated distribution when the truncation goes to infinity.",
  "abstract_shown": true,
  "affiliations": [
    "IRMA, CNRS and Université de Strasbourg",
    "D-MATH, ETH Zürich"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Barbara Dembin",
      "orcid": "0000-0003-1353-6122"
    },
    {
      "affs": [
        1
      ],
      "name": "Vincent Tassion"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nyb9d39rfnsn.bib",
  "cited_by": 6,
  "doi": "10.1214/25-aop1771",
  "fulltext_url": null,
  "id": "4nyb9d39rfnsn",
  "issns": [
    "0091-1798",
    "2168-894X"
  ],
  "landing_url": "https://hal.science/hal-05826940v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "0.math"
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W4294789860",
  "pdf_url": "https://hal.science/hal-05826940/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-30",
  "publisher": "Institute of Mathematical Statistics",
  "ris": "https://research.draconitic.com/paper/4nyb9d39rfnsn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05826940",
      "source": "hal",
      "url": "https://hal.science/hal-05826940v1"
    },
    {
      "first_seen": "2026-11-05T13:20:40Z",
      "native_id": "W4294789860",
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      "url": "http://arxiv.org/abs/2209.00999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Almost sharp sharpness for Poisson Boolean percolation",
  "title_text": "Almost sharp sharpness for Poisson Boolean percolation",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T13:20:40Z",
  "url": "https://research.draconitic.com/paper/4nyb9d39rfnsn",
  "venue": "The Annals of Probability",
  "versions": []
}