Clustering in a Continuum Percolation Model
- 1 June 1997
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 29 (2) , 327-336
- https://doi.org/10.2307/1428005
Abstract
We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters ofkballs (calledk-mers) in the system, first rigorously derived by Penrose [15]. Our integral expressions are free of inherent redundancies, making them more tractable for numerical evaluation. We also derive and evaluate an integral expression for the average volume ofk-mers.Keywords
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