Geodesic
Limit theorem for the size of an image of subset under compositions of random mappings
Diskretnaya Matematika, Tome 29 (2017) no. 1, pp. 17-26

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Let $\mathcal{X_N}$ be a set consisting of $N$ elements and $F_1,F_2,\ldots$ be a sequence of random independent equiprobable mappings $\mathcal{X_N}\to\mathcal{X_N}$. For a subset $S_0\subset \mathcal{X_N}$, $|S_0|=n$, we consider a sequence of its images $S_t=F_t(\ldots F_2(F_1(S_0))\ldots)$, $t=1,2\ldots$ The conditions on $n$, $t$, $N\to\infty$ under which the distributions of image sizes $|S_t|$ are asymptotically connected with the standard normal distribution are presented.
Keywords: random equiprobable mappings, compositions of random mappings, asymptotic normality. 
@article{DM_2017_29_1_a2,
     author = {A. M. Zubkov and A. A. Serov},
     title = {Limit theorem for the size of an image of subset under compositions of random mappings},
     journal = {Diskretnaya Matematika},
     pages = {17--26},
     publisher = {mathdoc},
     volume = {29},
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     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_1_a2/}
}
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A. M. Zubkov; A. A. Serov. Limit theorem for the size of an image of subset under compositions of random mappings. Diskretnaya Matematika, Tome 29 (2017) no. 1, pp. 17-26. http://geodesic.mathdoc.fr/item/DM_2017_29_1_a2/