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Diskr. Mat., 2017, Volume 29, Issue 1, Pages 17–26 (Mi dm1403)  

This article is cited in 4 scientific papers (total in 4 papers)

Limit theorem for the size of an image of subset under compositions of random mappings

A. M. Zubkov, A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/dm1403

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English version:
Discrete Mathematics and Applications, 2018, 28:2, 131–138

Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.214
Received: 14.07.2016

Citation: A. M. Zubkov, A. A. Serov, “Limit theorem for the size of an image of subset under compositions of random mappings”, Diskr. Mat., 29:1 (2017), 17–26; Discrete Math. Appl., 28:2 (2018), 131–138

Citation in format AMSBIB
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\vol 29
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\pages 17--26
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\jour Discrete Math. Appl.
\yr 2018
\vol 28
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\pages 131--138
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Zubkov, V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe $k$-kratnoi iteratsii sluchainogo ravnoveroyatnogo otobrazheniya”, Matem. vopr. kriptogr., 8:4 (2017), 63–74  mathnet  crossref  mathscinet  elib
    2. Kogan D. Manohar N. Boneh D., “T/Key: Second-Factor Authentication From Secure Hash Chains”, Ccs'17: Proceedings of the 2017 Acm Sigsac Conference on Computer and Communications Security, Assoc Computing Machinery, 2017, 983–999  crossref  isi  scopus
    3. A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Discrete Math. Appl., 28:5 (2018), 331–338  mathnet  crossref  crossref  isi  elib
    4. V. O. Mironkin, “Sloi v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 10:1 (2019), 73–82  mathnet  crossref
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