@article {IOPORT.06049232,
    author       = {Benjamini, Itai and Curien, Nicolas},
    title        = {Recurrence of the $\mathbb{Z}^d$-valued infinite snake via unimodularity.},
    year         = {2012},
    journal      = {Electronic Communications in Probability [electronic only]},
    volume       = {17},
    issn         = {1083-589X},
    pages        = {Paper No. 1, 10 p., electronic only},
    publisher    = {University of Washington, Washington},
    doi          = {10.1214/ECP.v17-1700},
    abstract     = {Summary: 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 $d \leq 4$.},
    identifier   = {06049232},
}