{"paper":{"title":"Time-dependent P\\'olya urn","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nadia Sidorova","submitted_at":"2018-07-12T22:03:03Z","abstract_excerpt":"We consider a time-dependent version of a P\\'olya urn containing black and white balls. At each time $n$ a ball is drawn from the urn at random and replaced in the urn along with $\\sigma_n$ additional balls of the same colour. The proportion of white balls converges almost surely to a random limit $\\Theta$, and $\\mathcal{D}=\\{\\Theta\\in\\{0,1\\}\\}$ denotes the event when one of the colours dominates. The phase transition, in terms of the sequence $(\\sigma_n)$, between the regimes ${\\mathbb P}(\\mathcal{D})=1$ and ${\\mathbb P}(\\mathcal{D})<1$ was obtained by R. Pemantle in 1990. We describe the pha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04844","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"}