{"paper":{"title":"On the length of an external branch in the Beta-coalescent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Arno Siri-Jegousse, Fabian Freund, Jean-Stephane Dhersin, Linglong Yuan","submitted_at":"2012-01-19T07:20:00Z","abstract_excerpt":"In this paper, we consider Beta$(2-{\\alpha},{\\alpha})$ (with $1<{\\alpha}<2$) and related ${\\Lambda}$-coalescents. If $T^{(n)}$ denotes the length of an external branch of the $n$-coalescent, we prove the convergence of $n^{{\\alpha}-1}T^{(n)}$ when $n$ tends to $ \\infty $, and give the limit. To this aim, we give asymptotics for the number $\\sigma^{(n)}$ of collisions which occur in the $n$-coalescent until the end of the chosen external branch, and for the block counting process associated with the $n$-coalescent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3983","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"}