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Subcritical regimes in the Poisson Boolean model of continuum percolation

Jean-Baptiste Gouéré

Published 2006-11-13, updated 2008-10-01Version 2

We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if $E(R^d)$ 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.

Comments: Published in at http://dx.doi.org/10.1214/07-AOP352 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2008, Vol. 36, No. 4, 1209-1220
Categories: math.PR
Subjects: 60K35, 60D05, 82B43
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