Invariance principle for the random conductance model

We study a continuous time random walk X in an environment of i.i.d. random conductances μe∈ [0,∞) in ℤd. We assume that ℙ(μe > 0) > pc, so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μ e. We prove a quenched invariance principle for X, and obtain Green's functions bounds and an elliptic Harnack inequality. © 2012 Springer-Verlag.