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.
Received 30.V.2016, 30.XI.2018
Bibliographic databases:
Document Type:
Article
UDC:519.212.2+519.719.2
Language: Russian
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
\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}
Linking options:
https://www.mathnet.ru/eng/mvk277
https://doi.org/10.4213/mvk277
https://www.mathnet.ru/eng/mvk/v10/i1/p73
This publication is cited in the following 4 articles:
V. O. Mironkin, “O raspredelenii dlin tsiklov v grafe k-kratnoi iteratsii ravnoveroyatnoi sluchainoi podstanovki”, PDM, 2023, no. 62, 5–12
V. O. Mironkin, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114
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
V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 10:3 (2019), 89–99
Citation in format AMSBIB
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