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Oriented Percolation Model

Illustration

Illustration

Definition

A d-dimensional discrete percolation model on a regular point lattice L = L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the so-called north-east oriented lattice L^⇀ obtained by orienting each edge of an arbitrary (perhaps unoriented) point lattice L in the direction of increasing coordinate-value. The above figure shows an example of a subset of a 2-dimensional oriented percolation model on the north-east lattice. Here, each edge has been deleted with probability 1 - p for some 0<=p<=1, independently of all other edges.

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