Document Type

Article

Publication Date

2009

Abstract

Let 𝓟 be a Poisson process of intensity 1 in a square Sn of area n. For a fixed integer k, join every point of 𝓟 to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that, for cccrit, Gn,⌊clogn⌋ is disconnected with probability tending to 1 as n →∞ and, for cccrit, Gn,⌊clogn⌋ is connected with probability tending to 1 as n →∞. This answers a question posed in Balister et al. (2005).

Publication Title

Advances in Applied Probability

Volume

41

Issue

1

First Page

1

Last Page

12

Required Publisher's Statement

Published by Project Euclid

DOI:10.1239/aap/1240319574

Comments

This is the authors' version of the article. The publisher version is at: http://projecteuclid.org/euclid.aap/1240319574

Included in

Mathematics Commons

Share

COinS