On Traversable Length inside Semi-Cylinder in 2D supercritical Bond Percolation

Details On Traversable Length inside Semi-Cylinder in 2D supercritical Bond Percolation On Traversable Length inside Semi-Cylinder in 2D supercritical Bond Percolation

2006-10-25

arxiv.org/abs/math/0610744v1

Mathematics

Probability

16 pages

Scientific paper

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.

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