On Traversable Length inside Semi-Cylinder in 2D supercritical Bond Percolation
Probability
2007-05-23 v1
Abstract
We investigate a limit theorem on traversable length inside semi-cylinder in the 2-dimensional supercritical Bernoulli bond percolation, which gives an extension of Theorem 2 in Grimmett(1981). This type of limit theorems was originally studied for the extinction time for the 1-dimensional contact process on a finite interval in Wagner and Anantharam(2005). Actually, our main result Theorem 2.1 is stated under a rather general 2-dimensional bond percolation setting.
Keywords
Cite
@article{arxiv.math/0610744,
title = {On Traversable Length inside Semi-Cylinder in 2D supercritical Bond Percolation},
author = {Nobuaki Sugimine and Masato Takei},
journal= {arXiv preprint arXiv:math/0610744},
year = {2007}
}
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16 pages