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July 2008 Subcritical regimes in the Poisson Boolean model of continuum percolation
Jean-Baptiste Gouéré
Ann. Probab. 36(4): 1209-1220 (July 2008). DOI: 10.1214/07-AOP352

Abstract

We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if E(Rd) is finite, where R denotes the radius of the balls around Poisson points and d denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.

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Jean-Baptiste Gouéré. "Subcritical regimes in the Poisson Boolean model of continuum percolation." Ann. Probab. 36 (4) 1209 - 1220, July 2008. https://doi.org/10.1214/07-AOP352

Information

Published: July 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1148.60077
MathSciNet: MR2435847
Digital Object Identifier: 10.1214/07-AOP352

Subjects:
Primary: 60D05, 60K35, 82B43

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • July 2008
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