{"paper":{"title":"An ergodic theorem for partially exchangeable random partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jim Pitman, Yuri Yakubovich","submitted_at":"2017-07-02T16:19:52Z","abstract_excerpt":"We consider shifts $\\Pi_{n,m}$ of a partially exchangeable random partition $\\Pi_\\infty$ of $\\mathbb{N}$ obtained by restricting $\\Pi_\\infty$ to $\\{n+1,n+2,\\dots, n+m\\}$ and then subtracting $n$ from each element to get a partition of $[m]:= \\{1, \\ldots, m \\}$. We show that for each fixed $m$ the distribution of $\\Pi_{n,m}$ converges to the distribution of the restriction to $[m]$ of the exchangeable random partition of $\\mathbb{N}$ with the same ranked frequencies as $\\Pi_\\infty$. As a consequence, the partially exchangeable random partition $\\Pi_\\infty$ is exchangeable if and only if $\\Pi_\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00313","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"}