@article{EJP456,
author = {Marek Biskup and Timothy Prescott},
title = {Functional CLT for Random Walk Among Bounded Random Conductances},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {Random conductance model, invariance principle, corrector, homogenization, heat kernel, percolation, isoperimetry},
abstract = {We consider the nearest-neighbor simple random walk on $Z^d$, $d\ge2$, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$. Apart from the requirement that the bonds with positive conductances percolate, we pose no restriction on the law of the $\omega$'s. We prove that, for a.e. realization of the environment, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. The quenched functional CLT holds despite the fact that the local CLT may fail in $d\ge5$ due to anomalously slow decay of the probability that the walk returns to the starting point at a given time.},
pages = {no. 49, 1323-1348},
issn = {1083-6489},
doi = {10.1214/EJP.v12-456},
url = {http://ejp.ejpecp.org/article/view/456}}