Abstract
We consider a random graph created by the long-range percolation on the nth stage finite subset of a fractal lattice called the pre-Sierpinski gasket. The long-range percolation is a stochastic model in which any pair of two points is connected by a random bond independently. On the random graph obtained as above, we consider a discrete-time random walk. We show that the mixing time of the random walk is of order \(2^{(s-d)n}\) if \(d<s<2d\) in a sense. Here, s is a parameter which determines the order of probabilities that random bonds exist, and \(d=\log 3/\log 2\) is the Hausdorff dimension of the pre-Sierpinski gasket.
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The author thanks to the referee for giving comments to the first version of the manuscript. The author was supported by JSPS KAKENHI Grant Number 16K17615.
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Misumi, J. The Mixing Time of a Random Walk on a Long-Range Percolation Cluster in Pre-Sierpinski Gasket. J Stat Phys 165, 153–163 (2016). https://doi.org/10.1007/s10955-016-1611-z
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DOI: https://doi.org/10.1007/s10955-016-1611-z