Geodesic
A Markov chain with number-theoretic limit distribution
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 17-24.

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Let an urn contain balls of white and black colors. After each step with probabilities equal to $\frac12$ 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. \def\acknowledgementname{Funding
Keywords: discrete Markov chains, iterations of random mappings, limit distributions, Minkowski function. 
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Andrey M. Zubkov; Kseniya A. Kolesnikova. A Markov chain with number-theoretic limit distribution. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 17-24. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a1/

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