{"paper":{"title":"Limiting distribution of the maximal distance between random points on a circle: A moments approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eckhard Schlemm","submitted_at":"2014-05-23T16:36:31Z","abstract_excerpt":"Motivated by the problem of computing the distribution of the largest distance $d_{\\max}$ between $n$ random points on a circle we derive an explicit formula for the moments of the maximal component of a random vector following a Dirichlet distribution with concentration parameters $(1,\\ldots,1)$. We use this result to give a new proof of the fact that the law of $n\\,d_{\\max}-\\log n$ converges to a Gumbel distribution as $n$ tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6114","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"}