Continuum percolation for Gibbs point processes

Kaspar Stucki (Universität Göttingen)

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.

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Pages: 1-10

Publication Date: August 7, 2013

DOI: 10.1214/ECP.v18-2837

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