{"paper":{"title":"On the shape of the typical Poisson-Voronoi cell in high dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Matthias Irlbeck, Tobias M\\\"uller, Zakhar Kabluchko","submitted_at":"2025-06-03T08:28:26Z","abstract_excerpt":"We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$-th root of the intensity parameter $\\lambda$ of the Poisson process times the volume of the unit ball, the inradius, outradius, diameter and mean width of the typical cell converge in probability to the constants $1/2, 1, 2, 2$ respectively, as the dimension $d\\to\\infty$. We also show that the width of the typical cell, when rescaled in the same way, is bounded between $2\\sqrt{5}/(2+\\sqrt{5})-o_d(1)$ and $3/2+o_d(1)$, with probability $1-o_d(1)$. These results in particular imply that, with prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02607","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02607/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}