Random walk on the high-dimensional IIC

Markus Heydenreich; Remco van der Hofstad; Tim Hulshof

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arXiv · 1207.7230

Random walk on the high-dimensional IIC

Markus Heydenreich·Remco van der Hofstad·Tim Hulshof

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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.

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BibTeX RIS

Markus Heydenreich, Remco van der Hofstad, Tim Hulshof. 2013-12-04. Random walk on the high-dimensional IIC. https://arxiv.org/abs/1207.7230

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