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 Diskr. Mat., 2019, Volume 31, Issue 4, Pages 38–52 (Mi dm1596)

Collisions and incidence of vertices and components in 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. Formulas for the distribution of the length of the aperiodicity segment of a arbitrary vertex with some restrictions are calculated. Exact expressions for the probability of belonging of two arbitrary vertices to a single connected component, of hitting by a arbitrary vertex the preimage set of another vertex and of occurrence of a collision in such graph are obtained.

Keywords: uniform random mapping, iteration of random mapping, aperiodicity segment, graph of a mapping, connected component, preimage, collision.

DOI: https://doi.org/10.4213/dm1596

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UDC: 519.212.2+519.719.2
Revised: 24.11.2019

Citation: V. O. Mironkin, “Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping”, Diskr. Mat., 31:4 (2019), 38–52

Citation in format AMSBIB
\Bibitem{Mir19} \by V.~O.~Mironkin \paper Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping \jour Diskr. Mat. \yr 2019 \vol 31 \issue 4 \pages 38--52 \mathnet{http://mi.mathnet.ru/dm1596} \crossref{https://doi.org/10.4213/dm1596} 

• http://mi.mathnet.ru/eng/dm1596
• https://doi.org/10.4213/dm1596
• http://mi.mathnet.ru/eng/dm/v31/i4/p38

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This publication is cited in the following articles:
1. V. O. Mironkin, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114
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