{"paper":{"title":"Limit Theorems for the Pitman-Yor Frequency Spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"math.PR","authors_text":"Ross Arthur Maller, Soudabeh Shemehsavar","submitted_at":"2026-07-26T00:42:44Z","abstract_excerpt":"We derive a general distribution formula applicable to a wide variety of Gibbs-type partitions and use it to obtain large sample results for linear combinations of the component frequency spectrum $(M_{jn})_{1\\le j\\le n}$ (in genetics, the allele frequency spectrum) associated with a random partitioning of $\\{1,2,\\ldots, n\\}$. The two-parameter Pitman-Yor sampling model is analysed in detail and asymptotic distributions of sums of the form $\\sum _{j=\\lf \\lambda n\\rf}^{\\lf \\mu n\\rf} M_{jn}$, $0<\\lambda\\le \\mu\\le 1$, are obtained. Our results suggest a possible functional limit theorem for $\\sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}