{
  "abstract": "We consider the superposition $S_n$ of $n$ i.i.d. simple point processes on $\\mathbb{R}^d$ and apply a dependent thinning $T_n$, where the retention probability of a point depends on its local neighbour count within a radius $r_n$. While superpositions under independent thinning converge to Poisson processes, we show that under a critical geometric scaling $n v_d r_n^d \\to τ\\in (0,\\infty)$, the local interactions are transformed in the limit into an inhomogeneous Poisson point process with modified intensity. We prove that the thinned sequence $T_n(S_n)$ converges to a Poisson process with a non-linearly modified intensity $\\tildeλ(x) = λ(x)α(τλ(x))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Statistics & Probability Letters 235 (2026), 110740",
  "arxiv": "2609.25733",
  "author_total": 1,
  "authors": [
    {
      "name": "Kateryna Hlyniana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adyf6xn0qsf2r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25733",
  "fulltext_url": null,
  "id": "adyf6xn0qsf2r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25733",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25733",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adyf6xn0qsf2r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25733",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25733"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A law of thin processes with neighbour-count thinning",
  "title_text": "A law of thin processes with neighbour-count thinning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/adyf6xn0qsf2r",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.spl.2026.110740",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}