Computation of Coverage Probabilities in a Spherical Germ-Grain Model

Ian Flint and Nicolas Privault
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Ian Flint: Nanyang Technological University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 2, 491-502

Abstract: Abstract We consider a spherical germ-grain model on ℝ d $\mathbb {R}^{d}$ in which the centers of the spheres are driven by a possibly non-Poissonian point process. We show that various covering probabilities can be expressed using the cumulative distribution function of the random radii on one hand, and distances to certain subsets of ℝ d $\mathbb {R}^{d}$ on the other hand. This result allows us to compute the spherical and linear contact distribution functions, and to derive expressions which are suitable for numerical computation. Determinantal point processes are an important class of examples for which the relevant quantities take the form of Fredholm determinants.

Keywords: Boolean model; Germ-grain model; Capacity functional; Multipoint probability function; Determinantal point process; 60G60; 60D05; 60G55 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-019-09741-5

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