Functional CLT for random walk among bounded random conductances

Details Functional CLT for random walk among bounded random conductances Functional CLT for random walk among bounded random conductances

2007-01-09

arxiv.org/abs/math/0701248v3

Electron. J. Probab. 12 (2007), Paper no. 49, 1323-1348

Mathematics

Probability

26 pages; to appear in EJP

Scientific paper

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 (cf math.PR/0611666).

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