Geodesic
Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a~Classical Problems with Balls
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 144-154

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Let $n$ balls be dropped at random into $N$ boxes. Each ball may fall into any box with the same probability $1/N$, independently of what, happens to the other balls. Let $\mu_0(n)$ be the number of empty boxes. We consider $\mu_0(n)$ as a random function of time parameter $n$. We prove that the distribution of random function $\mu_0(n)$ converges to the distribution of a Gaussian or Poisson process as $n$, $N\to\infty$. 
@article{TVP_1967_12_1_a15,
     author = {B. A. Sevast'yanov},
     title = {Convergence of the {Distribution} of the {Number} of {Empty} {Boxes} to {Gaussian} and {Poisson} {Processes} in {a~Classical} {Problems} with {Balls}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {144--154},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/}
}
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B. A. Sevast'yanov. Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a~Classical Problems with Balls. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 144-154. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/