Continuum percolation with steps in an annulus

Details Continuum percolation with steps in an annulus Continuum percolation with steps in an annulus

2005-03-24

arxiv.org/abs/math/0503544v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1869-1879

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000891 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000891

Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1 and let G_A be the random graph with vertex set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the area of A is large, then G_A almost surely has an infinite component. Moreover, if we fix \epsilon, increase r and let n_c=n_c(\epsilon) be the area of A when this infinite component appears, then n_c\to1 as \epsilon \to 0. This is in contrast to the case of a ``square'' annulus where we show that n_c is bounded away from 1.

Affiliated with

Also associated with

No associations

Rating

Continuum percolation with steps in an annulus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuum percolation with steps in an annulus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuum percolation with steps in an annulus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-587006