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 Tr. Mat. Inst. Steklova, 2000, Volume 228, Pages 236–245 (Mi tm503)

Simple Random Walks along Orbits of Anosov Diffeomorphisms

V. Y. Kaloshin, Ya. G. Sinai

Princeton University, Department of Mathematics

Abstract: We consider a Markov chain whose phase space is a $d$-dimensional torus. A point $x$ jumps to $x+\omega$ with probability $p(x)$ and to $x-\omega$ with probability $1-p(x)$. For Diophantine $\omega$ and smooth $p$ we prove that this Maslov chain has an absolutely continuous invariant measure and the distribution of any point after $n$ steps converges to this measure.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 224–233

Bibliographic databases:

UDC: 531.19
Language: English

Citation: V. Y. Kaloshin, Ya. G. Sinai, “Simple Random Walks along Orbits of Anosov Diffeomorphisms”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Tr. Mat. Inst. Steklova, 228, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 236–245; Proc. Steklov Inst. Math., 228 (2000), 224–233

Citation in format AMSBIB
\Bibitem{KalSin00} \by V.~Y.~Kaloshin, Ya.~G.~Sinai \paper Simple Random Walks along Orbits of Anosov Diffeomorphisms \inbook Problems of the modern mathematical physics \bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov \serial Tr. Mat. Inst. Steklova \yr 2000 \vol 228 \pages 236--245 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm503} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782584} \zmath{https://zbmath.org/?q=an:0985.60045} \transl \jour Proc. Steklov Inst. Math. \yr 2000 \vol 228 \pages 224--233 

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This publication is cited in the following articles:
1. Kaimanovich V.A., Kifer Y., Rubshtein B.Z., “Boundaries and harmonic functions for random walks with random transition probabilities”, Journal of Theoretical Probability, 17:3 (2004), 605–646
2. V. I. Senin, “Sojourn measures of random walks on deterministic sequences”, Theory Stoch. Process., 19(35):1 (2014), 91–99
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