Inhomogeneous Percolation Model

A -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 -dimensional shapes in  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.

REFERENCES

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