{
  "abstract": "Consider a random geometric graph with vertices given by a Poisson point process, and whose edges depend on independent marks corresponding to the vertices and pairs of vertices. In this paper, we study two related questions on this general model: the number of edge crossings in a projection of this graph, and its graph-theoretical planarity. We focus on models with heavy-tailed mark distributions, in particular with polynomial tails with arbitrary exponents. We show that the asymptotic behaviour varies significantly depending on this exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08395",
  "author_total": 2,
  "authors": [
    {
      "name": "Hanna Döring"
    },
    {
      "name": "Kinga Nagy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6evfcdeatb3e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08395",
  "fulltext_url": null,
  "id": "e6evfcdeatb3e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08395",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7212081536",
  "pdf_url": "https://arxiv.org/pdf/2609.08395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6evfcdeatb3e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08395"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Planarity and number of crossings in general models of random geometric graphs",
  "title_text": "Planarity and number of crossings in general models of random geometric graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/e6evfcdeatb3e",
  "venue": "arXiv",
  "versions": []
}