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

Homogenization theory of random walks among deterministic conductances