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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 4, Pages 701–708 (Mi tvp670)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Asymptotic behaviour of a number of groups of particles in a classical problem of permutation

G. I. Ivchenko, Yu. I. Medvedev

Moscow

Abstract: Let groups each of $m$ particles be distributed independently into $n$ cells so that particles of every group are distributed into different cells with all ${n\choose m}$ possible permutations having equal probabilities. A random variable $\nu_m(n,t)$ is introduced which is equal to the number of groups whose distribution leads to at least $t$ cells being occupied for the first time.
In this paper the whole spectrum of limit theorems is obtained and exact formulae as well as their asymptotic expressions as $n$, $t\to\infty$ of the mean and variance of random variables $\nu_m(n,t)$ are found.

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English version:
Theory of Probability and its Applications, 1966, 11:4, 619–626

Bibliographic databases:

Received: 19.10.1965

Citation: G. I. Ivchenko, Yu. I. Medvedev, “Asymptotic behaviour of a number of groups of particles in a classical problem of permutation”, Teor. Veroyatnost. i Primenen., 11:4 (1966), 701–708; Theory Probab. Appl., 11:4 (1966), 619–626

Citation in format AMSBIB
\Bibitem{IvcMed66}
\by G.~I.~Ivchenko, Yu.~I.~Medvedev
\paper Asymptotic behaviour of a~number of groups of particles in a~classical problem of permutation
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 4
\pages 701--708
\mathnet{http://mi.mathnet.ru/tvp670}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=208629}
\zmath{https://zbmath.org/?q=an:0171.39403}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 4
\pages 619--626
\crossref{https://doi.org/10.1137/1111068}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. I. Ivchenko, “How many samples does it take to see all the balls in an urn?”, Math. Notes, 64:1 (1998), 49–54  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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