The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment

Abstract

The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or higher-dimensional, finite range, transient random walks in mixing random environments. One of the advantages of this method over what has been used so far is that it is not restricted to i.i.d. environments.

arXiv comment22 pages. To appear in the Annals of Probability

Cited by in corpus (13)

• Random walks in dynamic random environments: A transference principle
• Random walk driven by the simple exclusion process
• Process-level quenched large deviations for random walk in random environment
• Random Dirichlet environment viewed from the particle in dimension $d\ge 3$
• Large deviations for random walk in a space--time product environment
• Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments
• Alternative proof for the localization of Sinai's walk
• Limit velocity and zero--one laws for diffusions in random environment
• Harmonic functions, h-transform and large deviations for random walks in random environments in dimensions four and higher
• On the Transient (T) condition for Random Walk in Strong Mixing Environment
• Almost exponential decay for the exit probability from slabs of ballistic RWRE
• Asymptotic direction for random walks in mixing random environments
• Special Examples of Diffusions in Random Environment