Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527282 | Stochastic Processes and their Applications | 2012 | 20 Pages |
Abstract
We consider the random conductance model where the underlying graph is an infinite supercritical Galton-Watson tree, and the conductances are independent but their distribution may depend on the degree of the incident vertices. We prove that if the mean conductance is finite, there is a deterministic, strictly positive speed v such that limnââ|Xn|n=v a.s. (here, |â
| stands for the distance from the root). We give a formula for v in terms of the laws of certain effective conductances and show that if the conductances share the same expected value, the speed is not larger than the speed of a simple random walk on Galton-Watson trees. The proof relies on finding a reversible measure for the environment observed by the particle.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Nina Gantert, Sebastian Müller, Serguei Popov, Marina Vachkovskaia,