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Matematicheskie Zametki, 1968, Volume 4, Issue 1, Pages 97–103 (Mi mzm6748)  

The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells

Yu. V. Bolotnikov

Steklov Mathematical Institute, Academy of Sciences of USSR
Abstract: We consider a case in which $n$ particles are distributed independently of one another in $N$ cells. We examine the behavior of the number of empty cells, $\mu_0(n)$, as a random function of the parameter $n$ when $n,N\to\infty$. We prove that for suitable variation of the time parameter, $\mu_0(n)$ will converge to a Gaussian process in the following cases: a) $n/N\to\infty$, $n/N-\ln N\to-\infty$; b) $n/N\to0$, $n^2/N\to\infty$.
Received: 17.01.1968
English version:
Mathematical Notes, 1968, Volume 4, Issue 1, Pages 546–550
DOI: https://doi.org/10.1007/BF01429819
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: Yu. V. Bolotnikov, “The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells”, Mat. Zametki, 4:1 (1968), 97–103; Math. Notes, 4:1 (1968), 546–550
Citation in format AMSBIB
\Bibitem{Bol68}
\by Yu.~V.~Bolotnikov
\paper The convergence to a~Gaussian process of the number of empty cells in the classical problem of distributing particles among cells
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 1
\pages 97--103
\mathnet{http://mi.mathnet.ru/mzm6748}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=233397}
\zmath{https://zbmath.org/?q=an:0165.20304}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 1
\pages 546--550
\crossref{https://doi.org/10.1007/BF01429819}
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