The Annals of Probability

Subcritical regimes in the Poisson Boolean model of continuum percolation

Jean-Baptiste Gouéré

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We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if E(Rd) 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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Ann. Probab., Volume 36, Number 4 (2008), 1209-1220.

First available in Project Euclid: 29 July 2008

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 82B43: Percolation [See also 60K35]

Continuum percolation Poisson Boolean model


Gouéré, Jean-Baptiste. Subcritical regimes in the Poisson Boolean model of continuum percolation. Ann. Probab. 36 (2008), no. 4, 1209--1220. doi:10.1214/07-AOP352.

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