Subcritical regimes in the Poisson Boolean model of continuum percolation

Details Subcritical regimes in the Poisson Boolean model of continuum percolation Subcritical regimes in the Poisson Boolean model of continuum percolation

2006-11-13

arxiv.org/abs/math/0611369v2

Annals of Probability 2008, Vol. 36, No. 4, 1209-1220

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP352 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP352

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.

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