Random walks in space time mixing environments

TL;DR

This paper proves that random walks in environments with exponential space-time mixing exhibit diffusive behavior, with their scaled limits converging to the Wiener measure, confirming a form of universality in such stochastic processes.

Contribution

It establishes almost sure diffusive scaling limits for random walks in exponentially mixing space-time environments, extending previous results to a broader class of random environments.

Findings

Random walks in exponentially mixing environments are diffusive.

Scaling limits of these walks converge to Wiener measure.

Results hold almost surely for the considered class of environments.

Abstract

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.