Geometric Properties of Poisson Matchings

Details Geometric Properties of Poisson Matchings Geometric Properties of Poisson Matchings

2009-09-03

arxiv.org/abs/0909.0575v1

Mathematics

Probability

21 pages

Scientific paper

Suppose that red and blue points occur as independent Poisson processes of equal intensity in R^d, and that the red points are matched to the blue points via straight edges in a translation-invariant way. We address several closely related properties of such matchings. We prove that there exist matchings that locally minimize total edge length in d=1 and d>=3, but not in the strip R x [0,1]. We prove that there exist matchings in which every bounded set intersects only finitely many edges in d>=2, but not in d=1 or in the strip. It is unknown whether there exists a matching with no crossings in d=2, but we prove positive answers to various relaxations of this question. Several open problems are presented.

Affiliated with

Also associated with

No associations

Rating

Geometric Properties of Poisson Matchings 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 Geometric Properties of Poisson Matchings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Properties of Poisson Matchings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663539