Asymptotics of the visibility function in the Boolean model
Probability
2011-01-06 v2
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.
Cite
@article{arxiv.0905.4874,
title = {Asymptotics of the visibility function in the Boolean model},
author = {Pierre Calka and Julien Michel and Sylvain Porret-Blanc},
journal= {arXiv preprint arXiv:0905.4874},
year = {2011}
}
Comments
23 pages