Random walks on Galton–Watson trees with random conductances
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.
Volume (Year): 122 (2012)
Issue (Month): 4 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1652-1671. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.