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 Fundam. Prikl. Mat., 2013, Volume 18, Issue 5, Pages 119–128 (Mi fpm1544)

The probability of successful allocation of particles in cells (the general case)

I. R. Kayumov, A. N. Chuprunov

Kazan Federal University, Kazan, Russia

Abstract: Let $p_{nN}$ be the probability of successful allocation of $n$ groups of particles in $N$ cells with the following assumptions: (a) each group contains $m$ particles and has allocation as a general allocation scheme; (b) each cell contains at most $r$ particles from the same group; (c) events connected with different groups are independent. We obtain an asymptotically exact bound of $p_{nN}$ as $n,N\to\infty$ such that $n/N$ is bounded. Applications to problems in error-correcting coding are considered.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:1, 88–95

Bibliographic databases:

UDC: 519.212.2+517.537

Citation: I. R. Kayumov, A. N. Chuprunov, “The probability of successful allocation of particles in cells (the general case)”, Fundam. Prikl. Mat., 18:5 (2013), 119–128; J. Math. Sci., 209:1 (2015), 88–95

Citation in format AMSBIB
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\paper The probability of successful allocation of particles in cells (the general case)
\jour Fundam. Prikl. Mat.
\yr 2013
\vol 18
\issue 5
\pages 119--128
\mathnet{http://mi.mathnet.ru/fpm1544}
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\transl
\jour J. Math. Sci.
\yr 2015
\vol 209
\issue 1
\pages 88--95
\crossref{https://doi.org/10.1007/s10958-015-2486-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938292740}

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This publication is cited in the following articles:
1. A. I. Afonina, I. R. Kayumov, A. N. Chuprunov, “Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells”, Discrete Math. Appl., 27:5 (2017), 277–286
2. A. I. Afonina, I. R. Kayumov, A. N. Chuprunov, “On the probability of the event: in $n$ generalized allocation schemes the volume of each cell does not exceed $r$”, Ufa Math. J., 8:2 (2016), 14–21
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