# Random Walk on the High-Dimensional IIC

@article{Heydenreich2012RandomWO,
title={Random Walk on the High-Dimensional IIC},
author={Markus Heydenreich and Remco van der Hofstad and Tim Hulshof},
journal={Communications in Mathematical Physics},
year={2012},
volume={329},
pages={57-115}
}
• Published 1 July 2012
• Mathematics
• Communications in Mathematical Physics
We study the asymptotic behavior of the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by Kumagai and Misumi (J Theor Probab 21:910–935, 2008). We do this by getting 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…
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This work constructs the incipient infinite cluster measure for high-dimensional percolation models in three different ways, extending previous work by the second-named author and Járai, and shows that each construction yields the same measure, indicating that the IIC is a robust object.

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We identify the scaling limit of the backbone of the high-dimensional incipient infinite cluster (IIC), both in the long- as well as in the finite-range setting. In the finite-range setting, this

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