Recurrence of Distributional Limits of Finite Planar Graphs

Details Recurrence of Distributional Limits of Finite Planar Graphs Recurrence of Distributional Limits of Finite Planar Graphs

2000-11-02

arxiv.org/abs/math/0011019v4

Electron.J.Probab.6:1-13,2001

Mathematics

Probability

Name of paper changed from "Unbiased Finite Planar Graphs are Asymptotically Recurrent". A discussion of intrinsic mass transp

Scientific paper

Suppose that $G_j$ is a sequence of finite connected planar graphs, and in each $G_j$ a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a distributional limit $G$ of such graphs. Assume that the vertex degrees of the vertices in $G_j$ are bounded, and the bound does not depend on $j$. Then after passing to a subsequence, the limit exists, and is a random rooted graph $G$. We prove that with probability one $G$ is recurrent. The proof involves the Circle Packing Theorem. The motivation for this work comes from the theory of random spherical triangulations.

Affiliated with

Also associated with

No associations

Rating

Recurrence of Distributional Limits of Finite Planar Graphs 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 Recurrence of Distributional Limits of Finite Planar Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recurrence of Distributional Limits of Finite Planar Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-111592