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 Mat. Vopr. Kriptogr.: Year: Volume: Issue: Page: Find

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

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

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Document Type: Article
UDC: 519.212.2+519.719.2

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{http://elibrary.ru/item.asp?id=37652162}