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2018 Non-triviality of the vacancy phase transition for the Boolean model
Mathew D. Penrose
Electron. Commun. Probab. 23: 1-8 (2018). DOI: 10.1214/18-ECP153

Abstract

In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean $d$-space with $d \geq 2$. We prove that whenever the radius distribution has a finite $d$-th moment, there exists a strictly positive value for the intensity such that the vacant region percolates.

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Mathew D. Penrose. "Non-triviality of the vacancy phase transition for the Boolean model." Electron. Commun. Probab. 23 1 - 8, 2018. https://doi.org/10.1214/18-ECP153

Information

Received: 22 January 2018; Accepted: 18 July 2018; Published: 2018
First available in Project Euclid: 31 July 2018

zbMATH: 1394.60101
MathSciNet: MR3841410
Digital Object Identifier: 10.1214/18-ECP153

Subjects:
Primary: 60G55, 60K35, 82B43

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