{"paper":{"title":"Limit Theorems Associated With The Pitman-Yor Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fuqing Gao, Shui Feng, Youzhou Zhou","submitted_at":"2016-02-26T16:10:36Z","abstract_excerpt":"The Pitman-Yor process is a random discrete measure. The random weights or masses follow the two-parameter Poisson-Dirichlet distribution with parameters $0<\\alpha<1, \\theta>-\\alpha$. The parameters $\\alpha$ and $\\theta$ correspond to the stable and gamma components, respectively. The distribution of atoms is given by a probability $\\nu$. In this article we consider the limit theorems for the Pitman-Yor process and the two-parameter Poisson-Dirichlet distribution. These include law of large numbers, fluctuations, and moderate or large deviation principles. The limiting procedures involve eithe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08382","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":""},"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"}