Abstract

A limit theorem is presented for random allocations.
For a fixed period we allocate $m$ balls into $N$ boxes.
We repeat the experiment throughout $n$ periods.
Let $p_q$ denote the probability that we do not place more than $q$ balls  into any of the $N$ boxes during any of the $n$ repetitions.
The limit of $p_q$ is determined when $m,n,N \to \infty$.

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