A lower bound for the critical probability in a certain percolation process.

by Theodore Edward Harris

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A study that considers the lattice in the Cartesian plane consisting of all points (x, y) such that either x or y is an integer (positive, negative, or zero). The sides of the unit squares are called links. Each link is designated "active" with probability p or "passive" with probability 1 - p, independently of all other links. It is shown that if <>, then the probability is 0 that there is a connected infinite set of active links.

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