{"paper":{"title":"The impatient collector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Anis Amri (IECL), Philippe Chassaing (IECL)","submitted_at":"2019-06-26T12:12:54Z","abstract_excerpt":"In the coupon collector problem with $n$ items, the collector needs a random number of tries $T_n\\simeq n\\ln n$ to complete the collection. Also, after $nt$ tries, the collector has secured approximately a fraction $\\zeta_\\infty(t)=1-e^{-t}$ of the complete collection, so we call $\\zeta_\\infty$ the (asymptotic) \\emph{completion curve}.  In this paper, for $\\nu>0$, we address the asymptotic shape $\\zeta (\\nu,.) $ of the completion curve under the condition $T_n\\leq \\left( 1+\\nu \\right) n$, i.e. assuming that the collection is \\emph{completed unlikely fast}. As an application to the asymptotic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11012","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"}