Invariance principle for the random conductance model under moment conditions

We consider a continuous time random walk on the lattice ${\mathbb{Z}}^d$ in an environment of random conductances, ${\mu }_{x,y}$. The law of the environment is assumed to be ergodic with respect to space shifts with $\mathbb{P}[0<{\mu }_{x,y}<\mathrm{\infty }]=1$. In this talk, I will explain how a quenched invariance principle can be established under suitable moment conditions. A key ingredient in the proof is to establish the sub-linearity of the corrector by means of Moser's iteration scheme.

This is joint work with Sebastian Andres (Univ. Bonn) and Jean-Dominique Deuschel (TU Berlin).