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.
Received 15.III.2017
Bibliographic databases:
Document Type:
Article
UDC:519.212.2+519.719.2
Language: Russian
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
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\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
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\crossref{https://doi.org/10.4213/mvk239}
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Linking options:
https://www.mathnet.ru/eng/mvk239
https://doi.org/10.4213/mvk239
https://www.mathnet.ru/eng/mvk/v8/i4/p63
This publication is cited in the following 7 articles:
V. O. Mironkin, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114
V. O. Mironkin, “Sloi v grafe k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 10:1 (2019), 73–82
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
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
V. O. Mironkin, V. G. Mikhailov, “O mnozhestve obrazov k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 9:3 (2018), 99–108
V. O. Mironkin, “Ob otsenkakh raspredeleniya dliny otrezka aperiodichnosti v grafe k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, PDM, 2018, no. 42, 6–17
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