The Annals of Probability

Subcritical regimes in the Poisson Boolean model of continuum percolation

Jean-Baptiste Gouéré

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Abstract

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.

Article information

Source
Ann. Probab., Volume 36, Number 4 (2008), 1209-1220.

Dates
First available in Project Euclid: 29 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1217360967

Digital Object Identifier
doi:10.1214/07-AOP352

Mathematical Reviews number (MathSciNet)
MR2435847

Zentralblatt MATH identifier
1148.60077

Subjects
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]

Keywords
Continuum percolation Poisson Boolean model

Citation

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. https://projecteuclid.org/euclid.aop/1217360967


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References

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