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Devroye and Lu showed that the maximum degree $\\Delta_n$ of $T_n$ satisfies $\\Delta_n/\\lfloor \\log_2 n\\rfloor \\to 1$ almost surely; Goh and Schmutz showed distributional convergence of $\\Delta_n - \\lfloor \\log_2 n \\rfloor$ along suitable subsequences. In this work we show how a version of Kingman's coalescent can be used to access much finer properties of the degree distribution in $T_n$.\n  "},"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":"1507.05981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T20:29:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"21445f385ae073163cf73d54a049da0dd8eb44b6dd51f1b3f4f18b58ed38703a","abstract_canon_sha256":"678f38d6cd4fb1c0f48d4e8627c2cc349df4637db716ba1db168a52d68d63676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:36.871035Z","signature_b64":"dXHicvZYjml104Oa0iQ58girZX+FGsZaipu+IUcSEs6Mg+vDR8lNcW7EObVhFmfaGMFnVHoxGBlt1i/Yv7U1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da6c23c2a2fc27771f5e40367962fef12f6b8f2159ee1922e0edd03c93c09563","last_reissued_at":"2026-05-18T00:08:36.870154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:36.870154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High degrees of random recursive trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Laura Eslava, Louigi Addario-Berry","submitted_at":"2015-07-21T20:29:04Z","abstract_excerpt":"For $n\\ge 1$, let $T_n$ be a random recursive tree on the vertex set $[n]=\\{1,\\ldots,n\\}$. 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