Recurrence of the $ \mathbb{Z}^d$-valued infinite snake via unimodularity
Probability
2014-05-28 v2
Abstract
We use the concept of unimodular random graph to show that the branching simple random walk on indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if .
Keywords
Cite
@article{arxiv.1107.1226,
title = {Recurrence of the $ \mathbb{Z}^d$-valued infinite snake via unimodularity},
author = {Itai Benjamini and Nicolas Curien},
journal= {arXiv preprint arXiv:1107.1226},
year = {2014}
}
Comments
Published version available at http://ecp.ejpecp.org/article/view/1700/2003