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Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 4, Pages 696–700 (Mi tvp669)  

This article is cited in 14 scientific papers (total in 14 papers)

Short Communications

Limit theorems in a scheme of disposal of particles in cells

B. A. Sevast'yanov

Moscow
Abstract: We consider two schemes of disposal of $n$ particles into $N$ cells. In scheme I each particle may fall into any cell with the same probability $1/N$ independently of what happens to the other particles. In scheme II $n$ particles are divided in $n/m$ groups each group containing $m$ particles. The groups are disposed at random into $N$ cells independently of each other all particles of any group being disposed in different cells. Theprobability of any disposal of $m$ particles of each group is equal to $1/С^m_N$. Let $\mu_r(\mu_r')$ be the number of cells containing exactly $r$ particles in scheme I (II). We prove that the limit theorems for $\mu_r$ and $\mu'_r$ as $n$, $N\to\infty$ are the same.
Received: 28.12.1965
English version:
Theory of Probability and its Applications, 1966, Volume 11, Issue 4, Pages 614–619
DOI: https://doi.org/10.1137/1111067
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. A. Sevast'yanov, “Limit theorems in a scheme of disposal of particles in cells”, Teor. Veroyatnost. i Primenen., 11:4 (1966), 696–700; Theory Probab. Appl., 11:4 (1966), 614–619
Citation in format AMSBIB
\Bibitem{Sev66}
\by B.~A.~Sevast'yanov
\paper Limit theorems in a scheme of disposal of particles in cells
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 4
\pages 696--700
\mathnet{http://mi.mathnet.ru/tvp669}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=203784}
\zmath{https://zbmath.org/?q=an:0171.39402}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 4
\pages 614--619
\crossref{https://doi.org/10.1137/1111067}
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  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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