{"paper":{"title":"Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander B. Reznikov, Edward B. Saff, Ian H. Sloan, Johann S. Brauchart, Robert S. Womersley, Yu Guang Wang","submitted_at":"2015-12-23T13:47:36Z","abstract_excerpt":"Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\\mathbb{S}^{d}\\subset\\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In particular, we derive asymptotics (as $N \\to \\infty$) for the expected moments of the radii of spherical caps associated with the facets of the convex hull of $N$ random points on $\\mathbb{S}^{d}$. We provide conjectures for the asymptotic distribution of the scaled radii of these spherical caps and the expected value of the largest of these radii (the covering"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07470","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}