English

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 E(Rd)E(R^d) is finite, where RR denotes the radius of the balls around Poisson points and dd 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)