Some Asymptotic Results for Occupancy Problems

Abstract

Suppose $n$ balls are placed into $N$ cells with arbitrary probabilities. Limit distributions for the number of empty cells are considered when $N \rightarrow \infty$ and $n \rightarrow \infty$ in such a way that $n/N \rightarrow \infty$. Limit distributions for the number of balls to achieve exactly $b$ empty cells are obtained for $N \rightarrow \infty$ with $b$ fixed and for $b \rightarrow \infty$ with $b/N \rightarrow 0$.