  We consider random walks in a balanced i.i.d. random environment in $Z^d$ for
$d\ge2$ and the corresponding discrete non-divergence form difference
operators. We first obtain an exponential integrability of the heat kernel
bounds. We then prove the optimal diffusive decay of the semigroup generated by
the heat kernel for $d\ge3$. As a consequence, we deduce a functional central
limit theorem for the environment viewed from the particle.
