Asymptotics of the visibility function in the Boolean model

Pierre Calka; Julien Michel; Sylvain Porret-Blanc

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arXiv · 0905.4874

Asymptotics of the visibility function in the Boolean model

Pierre Calka·Julien Michel·Sylvain Porret-Blanc

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Abstract

The aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region.

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Pierre Calka, Julien Michel, Sylvain Porret-Blanc. 2009-05-29. Asymptotics of the visibility function in the Boolean model. https://arxiv.org/abs/0905.4874

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