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Random walk on periodic trees. (English) Zbl 0888.60060

Summary: Following R. Lyons [Ann. Probab. 18, No. 3, 931-958 (1990; Zbl 0714.60089)] the author defines a periodic tree, restates its branching number and considers a biased random walk on it. In the case of a transient walk, she describes the walk-invariant random periodic tree and calculates the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric networks.

MSC:

60G50 Sums of independent random variables; random walks
60J45 Probabilistic potential theory

Citations:

Zbl 0714.60089
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