Invariance principle for random walks on dynamically averaging random conductances

Abstract

We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb{Z}$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations decrease according to a typical diffusive scaling and eventually approach constant unit conductances. The proof relies on a coupling with the standard continuous time simple random walk.