@article{EJP96,
author = {Itai Benjamini and Oded Schramm},
title = {Recurrence of Distributional Limits of Finite Planar Graphs},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {6},
year = {2001},
keywords = {Random triangulations, random walks, mass trasport, circle packing, volume growth.},
abstract = {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.},
pages = {no. 23, 1-13},
issn = {1083-6489},
doi = {10.1214/EJP.v6-96},
url = {http://ejp.ejpecp.org/article/view/96}}