On the speed of Random Walks among Random Conductances

2012/05/24 by Noam Berger, Berger, Noam, Michele Salvi +1
Mathematics · Physics and Astronomy · #60F20 (Secondary) #60K37 (Primary) 05C80 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:05C80 #msc:60F20 #msc:60K37

paper · pdf · doi:10.48550/arxiv.1205.5449

22 pages, 4 pictures

openalex publication_date 2012/05/24 · arxiv created 2013/12/17 · arxiv updated 2013/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider random walk among random conductances where the conductance environment is shift invariant and ergodic. We study which moment conditions of the conductances guarantee speed zero of the random walk. We show that if there exists α>1 such that E[log^α(ω_e)]<∞, then the random walk has speed zero. On the other hand, for each α>1 we provide examples of random walks with non-zero speed and random walks for which the limiting speed does not exist that have E[log^α(ω_e)]<∞.

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