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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.2855","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-14T15:40:42Z","cross_cats_sorted":[],"title_canon_sha256":"5282d09c2d72d6678f6e0423c8375803d36d54a070a0573c4648f8dbcea0a165","abstract_canon_sha256":"c7bd2429edea76643c193ed8834a2493d1a859c94064564cc025ca0141f200ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:46.262402Z","signature_b64":"N0nHT1Og6why/W6O+Xw2bLjWy70ROYcxwRZIJPRMM9XEwEx8wb8OGfKiiKcB4e5EmP4qXaWbIZ3Ml35LtbiSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e1efcde124da7245cc2abc917afb864d20d9c50336acd5dc27349b5b9ddbda9","last_reissued_at":"2026-05-18T03:42:46.261799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:46.261799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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