{"paper":{"title":"The hydrodynamic limit of beta coalescents that come down from infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Helmut H. Pitters, Luke Miller","submitted_at":"2016-11-19T00:05:37Z","abstract_excerpt":"We quantify the manner in which the beta coalescent $\\Pi=\\{ \\Pi(t), t\\geq 0\\},$ with parameters $a\\in (0, 1),$ $b>0,$ comes down from infinity. Approximating $\\Pi$ by its restriction $\\Pi^n$ to $[n]\\:= \\{1, \\ldots, n\\},$ the suitably rescaled block counting process $n^{-1}\\#\\Pi^n(tn^{a-1})$ has a deterministic limit, $c(t)$, as $n\\to\\infty.$ An explicit formula for $c(t)$ is provided in Theorem 1.\n  The block size spectrum $(\\mathfrak{c}_{1}\\Pi^n(t), \\ldots, \\mathfrak{c}_{n}\\Pi^n(t)),$ where $\\mathfrak{c}_{i}\\Pi^n(t)$ counts the number of blocks of size $i$ in $\\Pi^n(t),$ captures more refined"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06280","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"}