Scaling limits of random planar maps with large faces

Details Scaling limits of random planar maps with large faces Scaling limits of random planar maps with large faces

2009-07-19

arxiv.org/abs/0907.3262v2

Annals of Probability 2011, Vol. 39, No. 1, 1-69

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP549 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP549

We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index $\alpha\in(1,2)$. When the number $n$ of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process, which can be constructed from a centered stable process with no negative jumps and index $\alpha$. In particular, the profile of distances in the map, rescaled by the factor $n^{-1/2\alpha}$, converges to a random measure defined in terms of the distance process. With the same rescaling of distances, the vertex set viewed as a metric space converges in distribution as $n\to\infty$, at least along suitable subsequences, toward a limiting random compact metric space whose Hausdorff dimension is equal to $2\alpha$.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585813