Law of large numbers for ballistic random walks in dynamic random environments under lateral decoupling
arXiv:2205.00282 · doi:10.1214/23-AIHP1443
Abstract
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as a bound on the speed of dependence propagation, while the random walk is assumed to move ballistically with a speed larger than this bound. Applications include environments with strong space-time correlations such as the zero-range process and the asymmetric exclusion process.
33 pages. Accepted for publication in Annales de l'Institut Henri Poincaré, Probabilités et Statistiques