Electronic Communications in Probability

Continuum percolation for Gibbs point processes

Kaspar Stucki

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315606

Digital Object Identifier
doi:10.1214/ECP.v18-2837

Mathematical Reviews number (MathSciNet)
MR3091725

Zentralblatt MATH identifier
1323.60132

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

Keywords
Gibbs point process Percolation Boolean model Conditional intensity

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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