Geodesic
Simple Random Walks along Orbits of Anosov Diffeomorphisms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 236-245 
V. Y. Kaloshin; Ya. G. Sinai. Simple Random Walks along Orbits of Anosov Diffeomorphisms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 236-245. http://geodesic.mathdoc.fr/item/TM_2000_228_a17/
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     url = {http://geodesic.mathdoc.fr/item/TM_2000_228_a17/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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