On the speed of Random Walks among Random Conductances

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)]<\infty, 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)]<\infty.

22 pages, 4 pictures

References in corpus (3)

• Recent progress on the Random Conductance Model
• Recurrence of edge-reinforced random walk on a two-dimensional graph
• Shortest spanning trees and a counterexample for random walks in random environments

Cited by in corpus (2)

• Invariance principle for the random conductance model in a degenerate ergodic environment
• Random walk on a perturbation of the infinitely-fast mixing interchange process