Geodesics in large planar maps and in the Brownian map

Details Geodesics in large planar maps and in the Brownian map Geodesics in large planar maps and in the Brownian map

2008-04-18

arxiv.org/abs/0804.3012v2

Mathematics

Probability

64 pages, second version with minor corrections, and additional references and figures

Scientific paper

We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set S of all points that are connected to the root by more than one geodesic. The set S is dense in the Brownian map and homeomorphic to a non-compact real tree. Furthermore, for every x in S, the number of distinct geodesics from x to the root is equal to the number of connected components of the complement of {x} in S. In particular, points of the Brownian map can be connected to the root by at most three distinct geodesics. Our results have applications to the behavior of geodesics in large planar maps.

Affiliated with

Also associated with

No associations

Rating

Geodesics in large planar maps and in the Brownian map 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 Geodesics in large planar maps and in the Brownian map, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesics in large planar maps and in the Brownian map will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-304130