Mathematics – Probability
Scientific paper
2010-02-09
Mathematics
Probability
Scientific paper
Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components.
Deijfen Maria
Häggström Olle
Holroyd Alexander E.
No associations
LandOfFree
Percolation in invariant Poisson graphs with i.i.d. degrees 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 Percolation in invariant Poisson graphs with i.i.d. degrees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Percolation in invariant Poisson graphs with i.i.d. degrees will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-125297