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 $d \leq 4$.
Citation
Itai Benjamini. Nicolas Curien. "Recurrence of the $\mathbb{Z}^d$-valued infinite snake via unimodularity." Electron. Commun. Probab. 17 1 - 10, 2012. https://doi.org/10.1214/ECP.v17-1700
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