 Random walks on Galton–Watson trees with random conductancesNina Gantert, Sebastian Müller, Serguei Popov and Marina Vachkovskaia Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1652-1671 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 limn→∞|Xn|n=v a.s. (here, |⋅| 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. Keywords: Rate of escape; Environment observed by the particle; Effective conductance; Reversibility (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:4:p:1652-1671 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2012.01.004 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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