{
  "abstract": "We study void probabilities for stationary perturbed lattices with possibly dependent perturbations. Our main result gives a general upper bound in terms of two ingredients: the number of lattice sites having a uniformly positive probability of hitting the observation set, and the $α$-mixing rate of the perturbation field. For unions of lattice cubes, this yields explicit bounds without moment or regularity assumptions on the marginal distribution of the perturbations. As a consequence, we obtain quantitative estimates for growing bounded Borel sets with non-empty interior, including stretched-exponential decay under exponential mixing and polynomial decay under polynomial mixing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24650",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniela Flimmel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmcd299s6wnnc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24650",
  "fulltext_url": null,
  "id": "cmcd299s6wnnc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24650",
  "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",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7223020070",
  "pdf_url": "https://arxiv.org/pdf/2610.24650",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmcd299s6wnnc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24650",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24650"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Void probabilities for perturbed lattices under mixing",
  "title_text": "Void probabilities for perturbed lattices under mixing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/cmcd299s6wnnc",
  "venue": "arXiv",
  "versions": []
}