Inhomogeneous Percolation Model

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site percolation models) may have different probabilities of being open. This is in contrast to the typical bond and site percolation models which are homogeneous in the sense that openness of edges/vertices is determined by a random variable which is identically and independently distributed (i.i.d.).

Unsurprisingly, the breadth of continuum percolation theory allows one to adapt the above definition to models thereof. Such an adaptation could consist either of distributing d-dimensional shapes in R^d to points determined by inhomogeneous point processes-point processes with time-dependent realizations-or of utilizing non-uniform probability distributions to determine the properties of the shapes themselves.

See also

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

Cite this as:

Stover, Christopher. "Inhomogeneous Percolation Model." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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