Functional CLT for random walk among bounded random conductances

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dc.creatorBiskup, Marek
dc.creatorPrescott, Timothy M.
dc.date2007-01-09
dc.date2007-10-20
dc.date.accessioned2026-07-07T08:39:20Z
dc.date.available2026-07-07T08:39:20Z
dc.descriptionWe consider the nearest-neighbor simple random walk on $\Z^d$, $d\ge2$, driven by a field of i.i.d. random nearest-neighbor conductances $ω_{xy}\in[0,1]$. 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 $d\ge5$ due to anomalously slow decay of the probability that the walk returns to the starting point at a given time (cf math.PR/0611666).
dc.description26 pages; to appear in EJP
dc.identifierhttps://arxiv.org/abs/math/0701248
dc.identifierhttp://arxiv.org/abs/math/0701248
dc.identifierElectron. J. Probab. 12 (2007), Paper no. 49, 1323-1348
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141034
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K37; 60F05; 82C41
dc.titleFunctional CLT for random walk among bounded random conductances
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