Homogenization of non-divergence form operators in i.i.d. random environments

We study random walks in a balanced, i.i.d. random environment in ${\mathbb{Z}}^d$ for $d\ge 3$. We establish improved convergence rates for the homogenization of the Dirichlet problem associated with the corresponding non-divergence form difference operators, surpassing the $O(R^{-1})$ rate, which is expected to be optimal for environments with a finite range of dependence. In particular, the improved rates are $O(R^{-3\mathrm{/}2})$ when $d=3$, and $O(R^{-2}\log R)$ when $d\ge 4$.