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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Random walks on Galton-Watson trees with random conductances

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Author(s):
Gantert, Nina [1] ; Mueller, Sebastian [2] ; Popov, Serguei [3] ; Vachkovskaia, Marina [3]
Total Authors: 4
Affiliation:
[1] Tech Univ Munich, Fak Math, D-85748 Garching - Germany
[2] CMI Univ Provence, LATP, F-13453 Marseille 13 - France
[3] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Stochastic Processes and their Applications; v. 122, n. 4, p. 1652-1671, APR 2012.
Web of Science Citations: 3
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 nu such that lim(n ->infinity) vertical bar X-n/n vertical bar = nu a.s. (here, vertical bar.vertical bar stands for the distance from the root). We give a formula for nu 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. (c) 2012 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 10/16085-7 - Random walks in random environment
Grantee:Serguei Popov
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 09/08665-6 - Random walks on trees and branching random walks
Grantee:Serguei Popov
Support Opportunities: Regular Research Grants