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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 48–62
(Mi tvp3274)
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This article is cited in 19 scientific papers (total in 19 papers)
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 $\{1,2,\dots,n\}$ into itself. A random mapping from the set $\mathfrak M_n$ has a random number of components $\varkappa_n=\alpha_1+\dots+\alpha_n$, 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 $S_1,\dots,S_{\varkappa_n}$.
Received: 06.05.1975
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
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https://www.mathnet.ru/eng/tvp3274 https://www.mathnet.ru/eng/tvp/v21/i1/p48
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Abstract page: | 322 | Full-text PDF : | 189 |
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