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Disk Model


The disk model is the standard Boolean-Poisson model in two-dimensional continuum percolation theory. Its centers form a homogeneous Poisson point process X in R^2. At each point x in X, a random radius rho_x specifies a closed disk D_x (a two-dimensional closed ball). The radii are independent and identically distributed and independent of X (Last and Penrose 2017, pp. 166-167).

The closed disks which make up the disk model are known as random disks.


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, 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

Portions of this entry contributed by Christopher Stover

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References

Last, G. and Penrose, M. Lectures on the Poisson Process. Cambridge, England: Cambridge University Press, 2017. https://doi.org/10.1017/9781316104477.

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Disk Model

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Disk Model." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiskModel.html

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