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Diskr. Mat., 2004, Volume 16, Issue 1, Pages 9–13 (Mi dm139)  

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

Some classes of random mappings of finite sets, and nonhomogeneous branching processes

B. A. Sevast'yanov


Abstract: Let $X=\bigcup_{t=0}^TX_t$ be a finite set, where $X_t$, $t=1,2,\ldots,T$, are pairwise non-overlapping sets, $N_t=|X_t|$ be the cardinality of the set $X_t$, $t=0,1,\ldots,T$. Let $\mathcal F_1$ be the class of all mappings $f$ of the set $X'=X\setminus X_0$ into $X$ such that the image $y=f(x)\in X_{t-1}\cup X_t$ for any $x\in X_t$, $t=1,\ldots,T$. The cardinality of the set of all mappings of the class $\mathcal F_1$ is $\prod_{t=1}^T(N_{t-1}+N_t)^{N_t}$. With the use of non-homogeneous branching processes, we study some asymptotical properties of the uniformly distributed on $\mathcal F_1$ random mapping $f$ as $N_t\to\infty$, $t=1,2,\ldots,T$. Similar results are obtained for some other classes of random mappings $f$ of the set $X$.
This research was supported by the Russian Foundation for Basic Research, grant 02.01.00266, and the grant 1758.2003.1 of the President of Russian Federation for support of leading scientific schools.

DOI: https://doi.org/10.4213/dm139

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English version:
Discrete Mathematics and Applications, 2004, 14:1, 7–12

Bibliographic databases:

UDC: 519.2
Received: 11.11.2003

Citation: B. A. Sevast'yanov, “Some classes of random mappings of finite sets, and nonhomogeneous branching processes”, Diskr. Mat., 16:1 (2004), 9–13; Discrete Math. Appl., 14:1 (2004), 7–12

Citation in format AMSBIB
\Bibitem{Sev04}
\by B.~A.~Sevast'yanov
\paper Some classes of random mappings of finite sets, and nonhomogeneous branching processes
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 1
\pages 9--13
\mathnet{http://mi.mathnet.ru/dm139}
\crossref{https://doi.org/10.4213/dm139}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069986}
\zmath{https://zbmath.org/?q=an:1054.60090}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 1
\pages 7--12
\crossref{https://doi.org/10.1515/156939204774148785}


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    This publication is cited in the following articles:
    1. B. A. Sevast'yanov, “Convergence in distribution of random mappings of finite sets to branching processes”, Discrete Math. Appl., 15:2 (2005), 105–108  mathnet  crossref  crossref  mathscinet  zmath  elib
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