An inhomogeneous percolation model is a dimensional discrete
percolation model such that 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. In the usual homogeneous bond percolation
and site percolation models, the indicators
of openness are independent
and identically 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 points determined by inhomogeneous
point processes with spatially varying intensity
or of using probability distributions
for the properties of the shapes that vary with spatial location.
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 ,
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
Portions of this entry contributed by Christopher
Stover
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References Grimmett, G. Percolation, 2nd ed. Referenced on Wolfram|Alpha Inhomogeneous Percolation Model
Cite this as:
Weisstein, Eric W. , with contributions by Christopher Stover . "Inhomogeneous Percolation Model." From MathWorld https://mathworld.wolfram.com/InhomogeneousPercolationModel.html
Subject classifications
-dimensional discrete
percolation model such that 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. In the usual homogeneous bond percolation
and site percolation models, the indicators
of openness are independent
and identically distributed (i.i.d.).
-dimensional shapes in 
to points determined by inhomogeneous
point processes with spatially varying intensity
or of using probability distributions
for the properties of the shapes that vary with spatial location.
