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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 1, Pages 144–154 (Mi tvp695)

Short Communications

Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls

B. A. Sevast'yanov

Moscow

Abstract: 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 $n$, $N\to\infty$.

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English version:
Theory of Probability and its Applications, 1967, 12:1, 126–134

Bibliographic databases:

Citation: 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”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 144–154; Theory Probab. Appl., 12:1 (1967), 126–134

Citation in format AMSBIB
\Bibitem{Sev67} \by B.~A.~Sevast'yanov \paper Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a~Classical Problems with Balls \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 1 \pages 144--154 \mathnet{http://mi.mathnet.ru/tvp695} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=212856} \zmath{https://zbmath.org/?q=an:0183.20404} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 1 \pages 126--134 \crossref{https://doi.org/10.1137/1112016}