Recurrence of the ${\mathbb{Z}}^d$-valued infinite snake via unimodularity

Abstract

We use the concept of unimodular random graph to show that the branching simple random walk on ${\mathbb{Z}}^d$ indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if $d\le 4$.

Published version available at http://ecp.ejpecp.org/article/view/1700/2003

References in corpus (1)

• Ergodic Theory on Stationary Random Graphs