Electronic Communications in Probability

Continuum percolation for Gibbs point processes

Kaspar Stucki

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We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e., they do not percolate a.s. at low activity.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 67, 10 pp.

Accepted: 7 August 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Gibbs point process Percolation Boolean model Conditional intensity

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Stucki, Kaspar. Continuum percolation for Gibbs point processes. Electron. Commun. Probab. 18 (2013), paper no. 67, 10 pp. doi:10.1214/ECP.v18-2837. https://projecteuclid.org/euclid.ecp/1465315606

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