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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 48–62 (Mi tvp3274)

On disposal of particles in cells and random mappings of a finite set

V. F. Kolčin

Moscow

Abstract: We consider the uniform distribution on the set $\mathfrak M_n$ of all mappings of the finite set $\{1,2,…,n\}$ into itself. A random mapping from the set $\mathfrak M_n$ has a random number of components $\varkappa_n=\alpha_1+…+\alpha_n$, where $\alpha_r$ is the number of components of size $r$. We arrange the components according to their sizes and denote by $S_m$ the size of the $m$th component in the sequence. We prove a normal local limit theorem for $\varkappa_n$, a Poisson limit theorem for $\alpha_r$ and limit theorems for extreme and middle terms of the sequence $S_1,…,S_{\varkappa_n}$.

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English version:
Theory of Probability and its Applications, 1976, 21:1, 48–63

Bibliographic databases:

Citation: V. F. Kolčin, “On disposal of particles in cells and random mappings of a finite set”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 48–62; Theory Probab. Appl., 21:1 (1976), 48–63

Citation in format AMSBIB
\Bibitem{Kol76} \by V.~F.~Kol{\v{c}}in \paper On disposal of particles in cells and random mappings of a~finite set \jour Teor. Veroyatnost. i Primenen. \yr 1976 \vol 21 \issue 1 \pages 48--62 \mathnet{http://mi.mathnet.ru/tvp3274} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=404047} \zmath{https://zbmath.org/?q=an:0366.60015} \transl \jour Theory Probab. Appl. \yr 1976 \vol 21 \issue 1 \pages 48--63 \crossref{https://doi.org/10.1137/1121004} 

• http://mi.mathnet.ru/eng/tvp3274
• http://mi.mathnet.ru/eng/tvp/v21/i1/p48

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This publication is cited in the following articles:
1. A. N. Timashev, “Random mappings of finite sets with a known number of components”, Theory Probab. Appl., 48:4 (2004), 741–751