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Shift-coupling and a zero-one law for random walk in random environment. (English) Zbl 0804.60055

The paper discusses several aspects of shift-coupling for random walks in random environments. Three results on coupling of random walks in a random environment are formulated and proved. The starting point is that the invariant \(\sigma\)-field of the random walk (in a fixed environment) is trivial iff two random walks, starting from different sites, can be successfully shift-coupled.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks
60K05 Renewal theory
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References:

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