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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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Volume 26, Issue 3


Images of a finite set under iterations of two random dependent mappings

Aleksandr A. Serov
Published Online: 2016-07-15 | DOI: https://doi.org/10.1515/dma-2016-0015


Let N be a set of N elements and F1,G1,F2,G2, be a sequence of independent pairs of random dependent mappings NN such that Fk and Gk are random equiprobable mappings and P{Fk(x)=Gk(x)}=α for all xN and k = 1, 2, … For a subset S0N,|S0|=n, we consider a sequences of its images Sk=Fk(F2(F1(S0))), Tk=Gk(G2(G1(S0))), k = 1, 2 …, and a sequences of their unions SkTk and intersections SkTk, k = 1, 2 … We obtain two-sided inequalities for M|SkTk| and M|SkTk| such that upper and lower bounds are asymptotically equivalent if N,n,k, nk=o(N) and α=O1N.

Keywords: random mappings of finite sets; joint distributions; iterations of random mappings; Markov chain

Note: Originally published in Diskretnaya Matematika (2015) 27, No_4, 133–140 (in Russian).


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About the article

Received: 2015-10-30

Published Online: 2016-07-15

Published in Print: 2016-07-01

Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-50-00005

This work was supported by the Russian Science Foundation under grant no. 14-50-00005

Citation Information: Discrete Mathematics and Applications, Volume 26, Issue 3, Pages 175–181, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2016-0015.

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Андрей Михайлович Зубков, Andrei Mikhailovich Zubkov, Александр Александрович Серов, and Aleksandr Aleksandrovich Serov
Дискретная математика, 2017, Volume 29, Number 1, Page 17

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