{"paper":{"title":"A consistent Markov partition process generated from the paintbox process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Harry Crane","submitted_at":"2011-07-12T20:33:28Z","abstract_excerpt":"We study a family of Markov processes on $\\mathcal{P}^{(k)}$, the space of partitions of the natural numbers with at most $k$ blocks. The process can be constructed from a Poisson point process on $\\mathbb{R}^+\\times\\prod_{i=1}^k\\mathcal{P}^{(k)}$ with intensity $dt\\otimes\\varrho_{\\nu}^{(k)}$, where $\\varrho_{\\nu}$ is the distribution of the paintbox based on the probability measure $\\nu$ on $\\masspartition$, the set of ranked-mass partitions of 1, and $\\varrho_{\\nu}^{(k)}$ is the product measure on $\\prod_{i=1}^k\\mathcal{P}^{(k)}$. We show that these processes possess a unique stationary meas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2413","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"}