{"paper":{"title":"The limit distribution of the maximum probability nearest neighbor ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harro Walk, L\\'aszl\\'o Gy\\\"orfi, Norbert Henze","submitted_at":"2018-11-17T09:37:46Z","abstract_excerpt":"Let $X_1, \\ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large probability nearest neighbor balls. Denoting by $P_n$ the maximum probability measure of nearest neighbor balls, this limit theorem implies a Gumbel extreme value distribution for $nP_n - \\ln n$ as $n \\to \\infty$. Moreover, we derive a tight upper bound on the upper tail of the distribution of $nP_n - \\ln n$, which does not depend on $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07133","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":""},"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"}