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2007 Functional CLT for Random Walk Among Bounded Random Conductances
Marek Biskup, Timothy Prescott
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Electron. J. Probab. 12: 1323-1348 (2007). DOI: 10.1214/EJP.v12-456

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.

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Marek Biskup. Timothy Prescott. "Functional CLT for Random Walk Among Bounded Random Conductances." Electron. J. Probab. 12 1323 - 1348, 2007. https://doi.org/10.1214/EJP.v12-456

Information

Accepted: 25 October 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60093
MathSciNet: MR2354160
Digital Object Identifier: 10.1214/EJP.v12-456

Subjects:
Primary: 60K37
Secondary: 60F05, 82C41

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