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Slow movement of random walk in random environment on a regular tree. (English) Zbl 1124.60083

Summary: We consider a recurrent random walk in a random environment on a regular tree. Under suitable general assumptions concerning the distribution of the environment, we show that the walk exhibits an unusually slow movement: The order of magnitude of the walk in the first \(n\) steps is \((\log n)^3\).

MSC:

60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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