Quenched invariance principles for walks on clusters of percolation or among random conductances

Abstract

In this work we principally study random walk on the supercritical infinite cluster for bond percolation on ℤd. We prove a quenched functional central limit theorem for the walk when d ≥ 4. We also prove a similar result for random walk among i.i.d. random conductances along nearest neighbor edges of ℤd, when d ≥ 1.