This article is cited in 6 papers

Limit theorems in an occupancy problem

G. I. Ivčenko

Moscow

Abstract: There are $N$ cells into which particles are thrown independently of each other. Each particle falls into any fixed cell with probability $1/N$. Let $\nu_m(N,k)$ be the number of throwings after which $k$ cells will contain for the first time at least $m$ particles each.
This paper deals with the study of asymptotic behaviour of $\nu_m(N,k)$ as $N\to\infty$ under different assumptions about parameters $k$ and $m$. Limit distributions of $\nu_m(N,k)$ ($N\to\infty$) are found in the case when $m\to\infty$, $m/ln N\le C<\infty$, and either $k=\operatorname{const}$ or $N-k=\operatorname{const}$, or $k/N=\operatorname{const}$.

Received: 17.03.1969

 English version: Theory of Probability and its Applications, 1971, 16:2, 293–307

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