Geodesic
Correlation equations for the stable measure of a~Markov chain
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 536-540

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Each lamp of an infinite garland lights up with probability 1 if it and its neighbour both were lighting at the previous time moment, and with probability $\theta$ in the other case. It is shown that except for the trivial stable state “all the lamps are lighting”, for small $\theta$ there is only one stable probability measure $P_\theta$ on the state space of such systems and $P_\theta$ depends analitically on $\theta$. 
@article{TVP_1970_15_3_a10,
     author = {N. B. Vasil'ev},
     title = {Correlation equations for the stable measure of {a~Markov} chain},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {536--540},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a10/}
}
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N. B. Vasil'ev. Correlation equations for the stable measure of a~Markov chain. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 536-540. http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a10/