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# Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year

CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

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1569-3929
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# A Markov chain with number-theoretic limit distribution

Andrey M. Zubkov
/ Kseniya A. Kolesnikova
Published Online: 2016-04-26 | DOI: https://doi.org/10.1515/dma-2016-0010

## Abstract

Let an urn contain balls of white and black colors. After each step with probabilities equal to $\frac{1}{2}$ either the number of white balls is increased by the number of black balls or the number of black balls is increased by the number of white balls. Formulas for the first two moments of the total number of balls in an urn are derived and it is shown that the limiting distribution function of the proportion of the number of white balls in an urn coincides with the Minkowski number-theoretic function.

Originally published in Diskretnaya Matematika (2015) 27,.4, 17–24 (in Russian).

## References

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Lubotzky A., Pak I., “The product replacement algorithm and Kazdan’s property (T)”, J. Amer. Math. Soc., 14: 2 (2000), 347–363.Google Scholar

Published Online: 2016-04-26

Published in Print: 2016-04-01

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 2, Pages 125–130, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265,

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