{"paper":{"title":"The total external branch length of Beta-coalescents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Wakolbinger, G\\\"otz Kersting, Iulia Stanciu","submitted_at":"2012-12-25T17:42:12Z","abstract_excerpt":"For $1<\\alpha <2$ we derive the asymptotic distribution of the total length of {\\em external} branches of a Beta$(2-\\alpha, \\alpha)$-coalescent as the number $n$ of leaves becomes large. It turns out the fluctuations of the external branch length follow those of $\\tau_n^{2-\\alpha}$ over the entire parameter regime, where $\\tau_n$ denotes the random number of coalescences that bring the $n$ lineages down to one. This is in contrast to the fluctuation behavior of the total branch length, which exhibits a transition at $\\alpha_0 = (1+\\sqrt 5)/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6070","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"}