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Mat. Vopr. Kriptogr., 2017, Volume 8, Issue 4, Pages 63–74 (Mi mvk239)  

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

Distribution of the length of aperiodicity segment in the graph of $k$-fold iteration of uniform random mapping

A. M. Zubkova, V. O. Mironkinb

a Steklov Mathematical Institute of RAS, Moscow
b National Research University Higher School of Economics, Moscow

Abstract: The distribution of the length of the aperiodicity segment in a graph of $k$-fold iteration of random uniform mapping of a finite set is studied. Exact formulas for this distribution are obtained, the limit distribution of the normed length of aperiodicity segment is found for the case when the cardinality of the set tends to infinity.

Key words: equiprobable random mapping, iterations of random mapping, graph of a mapping, aperiodicity segment.

DOI: https://doi.org/10.4213/mvk239

Full text: PDF file (246 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.719.2
Received 15.III.2017

Citation: A. M. Zubkov, V. O. Mironkin, “Distribution of the length of aperiodicity segment in the graph of $k$-fold iteration of uniform random mapping”, Mat. Vopr. Kriptogr., 8:4 (2017), 63–74

Citation in format AMSBIB
\Bibitem{ZubMir17}
\by A.~M.~Zubkov, V.~O.~Mironkin
\paper Distribution of the length of aperiodicity segment in the graph of $k$-fold iteration of uniform random mapping
\jour Mat. Vopr. Kriptogr.
\yr 2017
\vol 8
\issue 4
\pages 63--74
\mathnet{http://mi.mathnet.ru/mvk239}
\crossref{https://doi.org/10.4213/mvk239}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3770675}
\elib{http://elibrary.ru/item.asp?id=32641309}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. V. O. Mironkin, V. G. Mikhailov, “O mnozhestve obrazov $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 9:3 (2018), 99–108  mathnet  crossref  elib
    3. V. O. Mironkin, “Ob otsenkakh raspredeleniya dliny otrezka aperiodichnosti v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, PDM, 2018, no. 42, 6–17  mathnet  crossref
    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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