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Clustering in a Continuum Percolation Model

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

J. Quintanilla  and
S. Torquato
J. Quintanilla*
Affiliation:
Princeton University
S. Torquato*
Affiliation:
Princeton University
*
∗ Postal address for both authors: Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544, USA.
∗ Postal address for both authors: Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544, USA.
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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 of k balls (called k-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 of k-mers.

Keywords

BOOLEAN MODELCLUSTER PROPERTIES

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 29 , Issue 2 , June 1997 , pp. 327 - 336
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This work was supported in part by the US Department of Energy, Office of Basic Energy Sciences under Grant No. DE-FG02-92ER14275, and by the MRSEC Program of the National Science Foundation under Award Number DMR-9400362.

J.Q. was partially supported under a National Science Foundation Graduate Research Fellowship. His present address is: Department of Mathematics, University of North Texas, Denton, Texas 76203, USA.

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