Random walk on the high-dimensional IIC
Abstract
We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.
Cite
@article{arxiv.1207.7230,
title = {Random walk on the high-dimensional IIC},
author = {Markus Heydenreich and Remco van der Hofstad and Tim Hulshof},
journal= {arXiv preprint arXiv:1207.7230},
year = {2013}
}
Comments
48 pages. Main difference with previous version: some proofs have been strengthened to work under milder assumptions. To appear in Commun. Math. Phys