Quenched invariance principle for simple random walk on percolation clusters
Berger, Noam ; Biskup, Marek
arXiv, 0503576 / Harvested from arXiv
Text on arXiv
We 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.
Publié le : 2005-03-24
Classification:  Mathematics - Probability,  Mathematical Physics,  60K37,  60F17,  82C41 
@article{0503576,
     author = {Berger, Noam and Biskup, Marek},
     title = {Quenched invariance principle for simple random walk on percolation
  clusters},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503576}
}

Berger, Noam; Biskup, Marek. Quenched invariance principle for simple random walk on percolation
  clusters. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503576/