  We study asymptotic laws of random walks on $\mathbb Z^d$ ($d\ge1$) in
deterministic reversible environments defined by an assignment of a positive
and finite conductance to each edge of $\mathbb Z^d$. The walk jumps across an
edge with probability proportional to its conductance. We identify a
deterministic set of conductance configurations for which an Invariance
Principle (i.e., convergence in law to Brownian motion under diffusive scaling
of space and time) provably holds. This set is closed under translations and
zero-density perturbations and carries all ergodic conductance laws subject to
certain moment conditions. The proofs are based on martingale approximations
whose control relies on the conversion of averages in time and physical space
under the deterministic environment to those in a suitable stochastic
counterpart. Our study sets up a framework for proofs of "deterministic
homogenization" in other motions in disordered media.
