Subcritical regimes in the Poisson Boolean model of continuum percolation

Gouéré, Jean-Baptiste

Ann. Probab., Tome 36 (2008) no. 1, p. 1209-1220 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-07-15
Classification: Continuum percolation, Poisson Boolean model, 60K35, 60D05, 82B43

@article{1217360967,
     author = {Gou\'er\'e, Jean-Baptiste},
     title = {Subcritical regimes in the Poisson Boolean model of continuum percolation},
     journal = {Ann. Probab.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 1209-1220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1217360967}
}

Gouéré, Jean-Baptiste. Subcritical regimes in the Poisson Boolean model of continuum percolation. Ann. Probab., Tome 36 (2008) no. 1, pp.  1209-1220. http://gdmltest.u-ga.fr/item/1217360967/