We consider discrete non-divergence form difference operators in an i.i.d.
random environment and the corresponding process--the random walk in a balanced
random environment in Zd. We first quantify the ergodicity of the
environment viewed 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 algebraic rate of convergence for
homogenization of the Dirichlet problems for both elliptic and parabolic
non-divergence form difference operators.Comment: 36 pages, 1 figur