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Clustering in a Continuum Percolation Model
J. Quintanilla and S. Torquato
Advances in Applied Probability
Vol. 29, No. 2 (Jun., 1997), pp. 327-336
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1428005
Page Count: 10
You can always find the topics here!Topics: Mathematical integrals, Arithmetic mean, Mathematical expressions, Mathematical functions, Radius of a sphere, Series expansion, Poisson process, Density, Numerical integration
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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 . 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.
Advances in Applied Probability © 1997 Applied Probability Trust