{"paper":{"title":"Asymptotics of the minimal clade size and related functionals of certain beta-coalescents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arno Siri-J\\'egousse, Linglong Yuan","submitted_at":"2013-11-22T17:13:18Z","abstract_excerpt":"This article shows the asymptotics of distributions of various functionals of the Beta$(2-\\alpha,\\alpha)$ $n$-coalescent process with $1<\\alpha<2$ when $n$ goes to infinity. This process is a Markov process taking {values} in the set of partitions of $\\{1, \\dots, n\\}$, evolving from the intial value $\\{1\\},\\cdots, \\{n\\}$ by merging (coalescing) blocks together into one and finally reaching the absorbing state $\\{1, \\dots, n\\}$. The minimal clade of $1$ is the block which contains $1$ at the time of coalescence of the singleton $\\{1\\}$. The limit size of the minimal clade of $1$ is provided. To"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5819","kind":"arxiv","version":2},"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"}