  We consider discrete non-divergence form difference operators in a random
environment and the corresponding process--the random walk in a balanced random
environment in $\mathbb{Z}^d$ with a finite range of dependence. We first
quantify the ergodicity of the environment from the point of view of the
particle. As a consequence, we quantify the quenched central limit theorem of
the random walk with an algebraic rate. Furthermore, we prove an algebraic rate
of convergence for the homogenization of the Dirichlet problems for both
elliptic and parabolic non-divergence form difference operators.
