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 Fundam. Prikl. Mat., 1996, Volume 2, Issue 4, Pages 1029–1043 (Mi fpm197)

Research Papers Dedicated to the Memory of B. V. Gnedenko

Transient dynamics of two interacting random strings

A. A. Zamyatin, A. A. Yambartsev

M. V. Lomonosov Moscow State University

Abstract: A finite string is just a sequence of symbols from finite alphabet. We consider a Markov chain with the state space equal to the set of all pairs of strings. Transition probabilities depend only on $d$ leftmost symbols in each string. Besides that, the jumps of the chain are bounded: the lengths of strings at subsequent moments of time cannot differ by more than some $d$. We consider the case when dynamics of Markov chain is transient, i.e. as $t\to\infty$ the lengths of both strings tend to infinity with probability 1. In this situation we prove stabilization law: the distribution of symbols close to left ends of strings tends to those of some random process.

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Bibliographic databases:
UDC: 519.217

Citation: A. A. Zamyatin, A. A. Yambartsev, “Transient dynamics of two interacting random strings”, Fundam. Prikl. Mat., 2:4 (1996), 1029–1043

Citation in format AMSBIB
\Bibitem{ZamYam96} \by A.~A.~Zamyatin, A.~A.~Yambartsev \paper Transient dynamics of two interacting random strings \jour Fundam. Prikl. Mat. \yr 1996 \vol 2 \issue 4 \pages 1029--1043 \mathnet{http://mi.mathnet.ru/fpm197} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1785770} \zmath{https://zbmath.org/?q=an:0916.60057} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Malyshev, “Interacting strings of symbols”, Russian Math. Surveys, 52:2 (1997), 299–326
2. A. A. Zamyatin, A. A. Yambartsev, “Classification of two interacting strings of symbols”, Russian Math. Surveys, 56:3 (2001), 597–598
3. Yambartsev, AA, “A stabilization law for two semi-infinite interacting strings of characters”, Bulletin of the Brazilian Mathematical Society, 34:3 (2003), 361
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