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arXiv · 1706.02197

Non-triviality of the vacancy phase transition for the Boolean model

Mathew D. Penrose
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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. 2017-06-07. Non-triviality of the vacancy phase transition for the Boolean model. https://arxiv.org/abs/1706.02197

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