Bipartite stable Poisson graphs on R

Details Bipartite stable Poisson graphs on R Bipartite stable Poisson graphs on R

2012-02-06

arxiv.org/abs/1202.1136v1

Mathematics

Probability

Scientific paper

Let red and blue points be distributed on $\mathbb{R}$ according to two independent Poisson processes $\mathcal{R}$ and $\mathcal{B}$ and let each red (blue) point independently be equipped with a random number of half-edges according to a probability distribution $\nu$ ($\mu$). We consider translation-invariant bipartite random graphs with vertex classes defined by the point sets of $\mathcal{R}$ and $\mathcal{B}$, respectively, generated by a scheme based on the Gale-Shapley stable marriage for perfectly matching the half-edges. Our main result is that, when all vertices have degree 2 almost surely, then the resulting graph does not contain an infinite component. The two-color model is hence qualitatively different from the one-color model, where Deijfen, Holroyd and Peres have given strong evidence that there is an infinite component. We also present simulation results for other degree distributions.

Affiliated with

Also associated with

No associations

Rating

Bipartite stable Poisson graphs on R 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 Bipartite stable Poisson graphs on R, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bipartite stable Poisson graphs on R will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-119506