Recurrence of Distributional Limits of Finite Planar Graphs
| dc.creator | Benjamini, Itai | |
| dc.creator | Schramm, Oded | |
| dc.date | 2000-11-02 | |
| dc.date | 2001-10-27 | |
| dc.date.accessioned | 2026-07-07T11:44:15Z | |
| dc.date.available | 2026-07-07T11:44:15Z | |
| dc.description | 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. | |
| dc.description | Name of paper changed from "Unbiased Finite Planar Graphs are Asymptotically Recurrent". A discussion of intrinsic mass transport was added | |
| dc.identifier | https://arxiv.org/abs/math/0011019 | |
| dc.identifier | http://arxiv.org/abs/math/0011019 | |
| dc.identifier | Electron.J.Probab.6:1-13,2001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/201534 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 82B41; 60J45; 52C26; 05C80 | |
| dc.title | Recurrence of Distributional Limits of Finite Planar Graphs | |
| dc.type | text |