{"paper":{"title":"The asymptotic distribution of the length of Beta-coalescent trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"otz Kersting","submitted_at":"2011-07-14T15:40:42Z","abstract_excerpt":"We derive the asymptotic distribution of the total length $L_n$ of a $\\operatorname {Beta}(2-\\alpha,\\alpha)$-coalescent tree for $1<\\alpha<2$, starting from $n$ individuals. There are two regimes: If $\\alpha\\le1/2(1+\\sqrt{5})$, then $L_n$ suitably rescaled has a stable limit distribution of index $\\alpha$. Otherwise $L_n$ just has to be shifted by a constant (depending on $n$) to get convergence to a nondegenerate limit distribution. As a consequence, we obtain the limit distribution of the number $S_n$ of segregation sites. These are points (mutations), which are placed on the tree's branches"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2855","kind":"arxiv","version":3},"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"}