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.
Additional Metadata
MSC Percolation (msc 82B43)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series CWI. Department of Modelling, Analysis and Computing [MAC]
Citation
Heydenreich, M, van der Hofstad, R.W, & Hulshof, W.J.T. (2012). Random walk on the high-dimensional IIC. CWI. Department of Modelling, Analysis and Computing [MAC]. CWI.