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Stationary measures for random walks in a random environment with random scenery. (English) Zbl 0926.60021
Summary: Let $$\Gamma$$ act on a countable set $$V$$ with only finitely many orbits. Given a $$\Gamma$$-invariant random environment for a Markov chain on $$V$$ and a random scenery, we exhibit, under certain conditions, an equivalent stationary measure for the environment and scenery from the viewpoint of the random walker. Such theorems have been very useful in investigations of percolation on quasi-transitive graphs.

##### MSC:
 60B99 Probability theory on algebraic and topological structures 60G50 Sums of independent random variables; random walks 28D15 General groups of measure-preserving transformations
##### Keywords:
Cayley graph; transitive graphs
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