The topological structure of scaling limits of large planar maps

Details The topological structure of scaling limits of large planar maps The topological structure of scaling limits of large planar maps

2006-07-22

arxiv.org/abs/math/0607567v2

Mathematics

Probability

45 pages Second version with minor modifications

Scientific paper

10.1007/s00222-007-0059-9

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.

Affiliated with

Also associated with

No associations

Rating

The topological structure of scaling limits of large planar maps 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 The topological structure of scaling limits of large planar maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The topological structure of scaling limits of large planar maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-301468