{
  "abstract": "We consider a Poisson process $η$ on a general Borel space with intensity measure $λ$ and a stopping set $Z$ depending on $η$. Generalizing earlier results we prove a spatial Markov property for $Z$. In fact we establish this property for the larger class of finitely insertion tolerant random sets, which include pointwise limits of stopping sets. Using the spatial Markov property of $η$, we derive several distributional identities for the restrictions of $η$ and $λ$ to $Z$ and the complement of $Z$. An important special case in Euclidean space is the convex hull of a finite Poisson process. In this case our results generalize classical (and also more recent) identities connecting the number of vertices and the volume of the convex hull.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06038",
  "author_total": 2,
  "authors": [
    {
      "name": "Günter Last"
    },
    {
      "name": "Ilya Molchanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ddx83vt683mf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06038",
  "fulltext_url": null,
  "id": "6ddx83vt683mf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06038",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7201851813",
  "pdf_url": "https://arxiv.org/pdf/2608.06038",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ddx83vt683mf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2608.06038",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06038"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Efron type identities for stopping sets and Poisson hulls",
  "title_text": "Efron type identities for stopping sets and Poisson hulls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/6ddx83vt683mf",
  "venue": "arXiv",
  "versions": []
}