Random walks on Galton-Watson trees with random conductances. (English) Zbl 1255.60178
A random walk is considered from the root of an infinite supercritical Galton-Watson tree with independent random conductances having distributions that may depend on the degrees of incident vertices. If the mean conductance is finite, it is proved that the speed of the random walk has almost surely a deterministic positive limit. By finding a reversible measure for the environment, the limiting speed is determined in terms of certain effective conductance distributions of subtrees. The limiting speed is also compared to the speed of a simple random walk on Galton-Watson trees. Explicit results for binary trees are used to illustrate the influence of the random environment on the speed of the random walk.
Reviewer: Ove Frank (Stockholm)
MSC:
| 60K37 | Processes in random environments |
| 05C81 | Random walks on graphs |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
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