Recurrence of the mathbb{Z}^d-valued infinite snake via unimodularity
classification
🧮 math.PR
keywords
mathbbrandombranchingconceptconditionedcriticalgalton-watsongeometric
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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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