A quantitative central limit theorem for the random walk among random conductances

Abstract

We consider the random walk among random conductances on $\mathbb{Z}^d$. We assume that the conductances are independent, identically distributed and uniformly bounded away from $0$ and infinity. We obtain a quantitative version of the central limit theorem for this random walk, which takes the form of a Berry-Esseen estimate with speed $t^{-1/10}$ for $d \le 2$, and speed $t^{-1/5}$ for $d \ge 3$, up to logarithmic corrections.