{"paper":{"title":"Urns with simultaneous drawing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Micka\\\"el Launay","submitted_at":"2012-01-17T12:29:18Z","abstract_excerpt":"In classical urn models, one usually draws one ball with replacement at each time unit and then adds one ball of the same colour. Given a weight sequence $(w_k)_{k\\in\\N}$, the probability of drawing a ball of a certain colour is proportional to $w_k$ where $k$ is the number of balls of this colour. A classical result states that an urn fixates on one colour after a finite time if an only if $\\sum_{0}^\\infty w_k^{-1} < \\infty$. In this paper we shall study the case when at each time unit we draw with replacement a number $d\\in\\N$ of balls and then add $d$ new balls of matching colours. The main"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3495","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"}