Geodesic
On multiple repetitions of long tuples in a Markov chain
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 117-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $X_0,X_1,\dots$ be a simple ergodic Markov chain with $N$ states and $\tilde\xi_{n,k}^{(m)}(s)$ be the number of $m$-series of $k$-repetitions of $s$-tuples in the chain segment $X_0,X_1,\dots,X_{n+s+m}$. The sufficient conditions for the distribution of the vector $\tilde\Xi_{n,k,M}(s)=(\tilde\xi_{n,k}^{(1)}(s),\dots,\tilde\xi_{n,k}^{(M)}(s))$ to converge to the multidimensional Poisson distribution are found. This permits to prove limit theorems for the distributions of some random variables connected with $\tilde\Xi_{n,k,M}(s)$. 
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V. G. Mikhailov; A. M. Shoitov. On multiple repetitions of long tuples in a Markov chain. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 117-133. http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a6/

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