Random walks on Galton-Watson trees with random conductances

Autor(es)

Gantert, Nina ^[1] ; Mueller, Sebastian ^[2] ; Popov, Serguei ^[3] ; Vachkovskaia, Marina ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 122, n. 4, p. 1652-1671, APR 2012.
• Citações Web of Science: 4

Resumo

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)

• Processo FAPESP: 09/08665-6 - Passeios aleatórios nas árvores e passeios aleatórios com ramificação
• Beneficiário: Serguei Popov
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/16085-7 - Passeios aleatórios em meios aleatórios
• Beneficiário: Serguei Popov
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional