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Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 1, Pages 73–82 (Mi mvk277)  

This article is cited in 3 scientific papers (total in 3 papers)

Layers of the graph of $k$-fold iteration of the uniform random mapping

V. O. Mironkin

National Research University Higher School of Economics, Moscow

Abstract: The probabilistic characteristics of the graph of $k$-fold iteration of uniform random mapping are studied. Exact expressions and estimates for the distribution of the distances from the vertices to cycles are obtained. Formulas for expected values of the numbers of vertices on the given distance from cycles and for the distribution function of the height of a random vertex are derived.

Key words: uniform random mapping, iteration of random mapping, graph of a mapping, layer in a graph, cyclic vertices.

DOI: https://doi.org/10.4213/mvk277

Full text: PDF file (174 kB)
References: PDF file   HTML file

UDC: 519.212.2+519.719.2
Received 30.V.2016, 30.XI.2018

Citation: V. O. Mironkin, “Layers of the graph of $k$-fold iteration of the uniform random mapping”, Mat. Vopr. Kriptogr., 10:1 (2019), 73–82

Citation in format AMSBIB
\Bibitem{Mir19}
\by V.~O.~Mironkin
\paper Layers of the graph of $k$-fold iteration of the uniform random mapping
\jour Mat. Vopr. Kriptogr.
\yr 2019
\vol 10
\issue 1
\pages 73--82
\mathnet{http://mi.mathnet.ru/mvk277}
\crossref{https://doi.org/10.4213/mvk277}
\elib{https://elibrary.ru/item.asp?id=37652162}


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  • https://doi.org/10.4213/mvk277
  • http://mi.mathnet.ru/eng/mvk/v10/i1/p73

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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. V. O. Mironkin, “Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping”, Discrete Math. Appl., 31:4 (2021), 259–269  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 10:3 (2019), 89–99  mathnet  crossref
    3. V. O. Mironkin, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114  mathnet  crossref
  • Математические вопросы криптографии
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