English

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 Zd\mathbb{Z}^{d} indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if d4d \leq 4.

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