Subcritical regimes in the Poisson Boolean model of continuum percolation
Probability
2008-10-03 v2
Abstract
We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if is finite, where denotes the radius of the balls around Poisson points and denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.
Keywords
Cite
@article{arxiv.math/0611369,
title = {Subcritical regimes in the Poisson Boolean model of continuum percolation},
author = {Jean-Baptiste Gouéré},
journal= {arXiv preprint arXiv:math/0611369},
year = {2008}
}
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)