{
  "abstract": "Ideal Poisson--Voronoi tessellations are random tessellations that arise as limits of Voronoi diagrams for Poisson point processes as their intensity tends to zero. For the Riemannian metric on a symmetric space of higher rank, Frączyk, Mellick, and Wilkens (arXiv:2307.01194) proved that the corresponding ideal Poisson--Voronoi tessellation is almost surely completely connected, with an unbounded side between any two cells. This contrasts sharply with the geometry of ideal Poisson--Voronoi tessellations in hyperbolic spaces studied by D'Achille, Curien, Enriquez, Lyons, and Ünel (arXiv:2303.16831). In this paper we introduce and study ideal Poisson--Voronoi tessellations for Finsler metrics on higher rank symmetric spaces. We show that ideal Poisson--Voronoi tessellations with respect to polyhedral Finsler metrics can exhibit either behavior seen in these previous works: generically they resemble the hyperbolic case, where almost surely all cells have bounded sides. We further introduce the ideal Selberg--Poisson--Voronoi tessellation of the space of positive definite symmetric matrices, which has particularly nice properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17045",
  "author_total": 3,
  "authors": [
    {
      "name": "Colin Davalo"
    },
    {
      "name": "J. Maxwell Riestenberg"
    },
    {
      "name": "Anna Wienhard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80tf6cypanhyd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17045",
  "fulltext_url": null,
  "id": "80tf6cypanhyd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17045",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221813436",
  "pdf_url": "https://arxiv.org/pdf/2610.17045",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80tf6cypanhyd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17045",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17045"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Ideal Poisson--Voronoi tessellations for Finsler metrics on symmetric spaces",
  "title_text": "Ideal Poisson--Voronoi tessellations for Finsler metrics on symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/80tf6cypanhyd",
  "venue": "arXiv",
  "versions": []
}