Continuum percolation for Gibbs point processes

Stucki, Kaspar (2013). Continuum percolation for Gibbs point processes. Electronic communications in probability, 18(67), pp. 1-10. Institute of Mathematical Statistics 10.1214/ECP.v18-2837

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Stucki, Kaspar

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

1083-589X

Publisher:

Institute of Mathematical Statistics

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

01 Apr 2014 03:22

Last Modified:

06 Dec 2014 18:58

Publisher DOI:

10.1214/ECP.v18-2837

ArXiv ID:

1305.0492

BORIS DOI:

10.7892/boris.41525

URI:

https://boris.unibe.ch/id/eprint/41525

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