Work

Asymptotics of the visibility function in the Boolean model

Year: 2009

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.0905.4874

Authors: Calka, Pierre, Michel, Julien, Porret-Blanc, Sylvain

Institutions: Mathématiques Appliquées à Paris 5, École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1646578288

Cites: 20

Cited by: 4

Related to: 10