English

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

R2 v1 2026-06-21T13:07:37.548Z