{"paper":{"title":"Poisson-Delaunay approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Strotmann, Matthias Reitzner","submitted_at":"2024-10-30T13:30:14Z","abstract_excerpt":"For a Borel set $A$ and a stationary Poisson point process $\\eta_t$ in $\\mathbb R^d$ of intensity $t>0$, the Poisson-Delaunay approximation $ A_{\\eta_t}$ of $A$ is the union of all Delaunay cells generated by $\\eta_t$ with center in $A$. It is shown that $\\lambda_d(A_{\\eta_t})$ is an unbiased estimator for $\\lambda_d(A)$, variance bounds and a quantitative central limit theorem are given. The asymptotic behaviour of the symmetric difference $\\lambda_d(A\\Delta A_{\\eta_t})$ is derived as $t \\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23003","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/2410.23003/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"}