Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces
Abstract
The Poisson Boolean percolation on a metric measure space is one of the percolation models. Intuitively, this model is obtained by collecting random balls whose centers form a Poisson point process. In 2008, Gou\'er\'e proved that for n ≥ 2, the Poisson Boolean percolation on Rn has the subcritical regime if and only if the radius distribution has finite n-th moment. In this paper, we extend Gou\'er\'e's result to Ahlfors regular metric measure spaces.
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