赠券收集问题中成组抽取的渐近结果
概率论
2026-05-11 v1
摘要
本文探讨了均匀分布下成组抽取的赠券收集问题中期望抽取次数的渐近行为。在此变体中，每次抽取包含从个赠券集合中均匀随机选取的个不同赠券组成的包。我们重点关注包大小的三种情形：(i) 常数，(ii) 与成正比，以及(iii) “非常接近”。对于每种情形，我们给出了期望收集时间的精确渐近表达式。
引用
@article{arxiv.2605.06953,
title = {Asymptotic Results for Uniform Group Drawing in the Coupon Collector's Problem},
author = {Daniel Berend and Tomer Sher},
journal= {arXiv preprint arXiv:2605.06953},
year = {2026}
}
备注
This article and arXiv:2509.17201 together supersede the original preprint, following their acceptance as two separate papers in Stochastic Models. This part focuses on asymptotic results for uniform group drawing in the coupon collector's problem