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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
DOI: 10.2307/1428005
Stable URL: http://www.jstor.org/stable/1428005
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Clustering in a Continuum Percolation Model
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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.

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