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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 49 open journal systems 


Functional CLT for random walk among bounded random conductances

Marek Biskup, UCLA
Timothy M Prescott, UCLA


Abstract
We consider the nearest-neighbor simple random walk on Zd, d≥2, driven by a field of i.i.d. random nearest-neighbor conductances ωxy∈[0,1]. Apart from the requirement that the bonds with positive conductances percolate, we pose no restriction on the law of the ω'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≥5 due to anomalously slow decay of the probability that the walk returns to the starting point at a given time.


Full text: PDF

Pages: 1323-1348

Published on: October 25, 2007
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Electronic Journal of Probability. ISSN: 1083-6489