Quenched invariance principle for simple random walk on percolation clusters

Simple item page
dc.creatorBerger, Noam
dc.creatorBiskup, Marek
dc.date2005-03-25
dc.date2006-02-20
dc.date.accessioned2026-07-07T07:53:20Z
dc.date.available2026-07-07T07:53:20Z
dc.descriptionWe consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\Z^d$ with $d\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a square-integrable martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.
dc.description38 pages (PTRF format) 4 figures. Version to appear in PTRF
dc.identifierhttps://arxiv.org/abs/math/0503576
dc.identifierhttp://arxiv.org/abs/math/0503576
dc.identifierProbab. Theory Rel. Fields 137 (2007), no. 1-2, 83-120
dc.identifierdoi:10.1007/s00440-006-0498-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126213
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K37; 60F17; 82C41
dc.titleQuenched invariance principle for simple random walk on percolation clusters
dc.typetext

Files

Collections

arXiv