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arXiv · 1308.4549

Upper Bound for Critical Probability of Site Percolation on Triangular Lattice

Marko Pujic
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Abstract

In site percolation, vertices (sites) of a graph are open with probability p, and there is critical p, for which open vertices form an open path the long way across a graph, so a vertex at the origin is a part of an infinite connected open vertex set. Smirnov found that for triangular lattice critical p is 0.5, but there is the traversal, from the origin upwards, so that an infinite connected open vertex set exists for critical p=0.3535.

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Marko Pujic. 2013-08-21. Upper Bound for Critical Probability of Site Percolation on Triangular Lattice. https://arxiv.org/abs/1308.4549

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