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AB Percolation


An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom either of type A or of type B, that there is a probability p that any given vertex is occupied by an atom of type A, and that different vertices are occupied independently of each other.

In this model, a graph edge of L is said to be open if its end vertices are occupied by atoms of different types and is said to be closed otherwise. The idea is based on the hypothesis that dissimilar atoms bond together whereas similar atoms repel one another.

This model is sometimes studied under the title antipercolation.


See also

Bernoulli Percolation Model, Bond Percolation, Boolean Model, Boolean-Poisson Model, Bootstrap Percolation, Cayley Tree, Cluster, Cluster Perimeter, Continuum Percolation Theory, Dependent Percolation, Discrete Percolation Theory, Disk Model, First-Passage Percolation, Germ-Grain Model, Inhomogeneous Percolation Model, Lattice Animal, Long-Range Percolation Model, Mixed Percolation Model, Oriented Percolation Model, Percolation, Percolation Theory, Percolation Threshold, Polyomino, Random-Cluster Model, Random-Connection Model, Random Walk, s-Cluster, s-Run, Site Percolation

This entry contributed by Christopher Stover

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References

Grimmett, G. Percolation, 2nd ed. Berlin: Springer-Verlag, 1999.

Cite this as:

Stover, Christopher. "AB Percolation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ABPercolation.html

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