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

   
@article{ECP1700,
	author = {Itai Benjamini and Nicolas Curien},
	title = {Recurrence of the $\mathbb{Z}^d$-valued infinite snake via unimodularity},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Galton-Watson trees; random snake; recurrence},
	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 $d \leq 4$.},
	pages = {no. 1, 1-10},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-1700},    
        url = {http://ecp.ejpecp.org/article/view/1700}}