A monotonicity property for random walk in a partially random environment
Probability
2016-11-25 v4
Abstract
We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment.
Cite
@article{arxiv.1005.0927,
title = {A monotonicity property for random walk in a partially random environment},
author = {Mark Holmes and Rongfeng Sun},
journal= {arXiv preprint arXiv:1005.0927},
year = {2016}
}
Comments
Revised version. To appear in Stochastic Processes and Their Applications