{"paper":{"title":"Rate of Convergence and Large Deviation for the Infinite Color P\\'olya Urn Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antar Bandyopadhyay, Debleena Thacker","submitted_at":"2013-10-21T22:49:01Z","abstract_excerpt":"In this work we consider the \\emph{infinite color urn model} associated with a bounded increment random walk on $\\Zbold^d$. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the expected configuration of the urn at time $n$ with appropriate centering and scaling is of the order ${\\mathcal O}\\left(\\frac{1}{\\sqrt{\\log n}}\\right)$. Moreover we derive bounds similar to the classical Berry-Essen bound. Further we show that for the expected configuration a \\emph{large deviation principle (LDP)} holds with a good rate function and speed $\\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5751","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"}