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

Itai Benjamini; Nicolas Curien

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

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arxiv 1107.1226 v2 pith:YSCF6MUY submitted 2011-07-06 math.PR

Itai Benjamini , Nicolas Curien This is my paper · ORCID

classification math.PR

keywords mathbbrandombranchingconceptconditionedcriticalgalton-watsongeometric

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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 $d \leq 4$.

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