Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces

Yutaka Takeuchi

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arXiv · 2410.23859

Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces

Yutaka Takeuchi

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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\'{e}r\'{e} proved that for $n \geq 2$, the Poisson Boolean percolation on $\mathbb{R}^n$ has the subcritical regime if and only if the radius distribution has finite $n$-th moment. In this paper, we extend Gou\'{e}r\'{e}'s result to Ahlfors regular metric measure spaces.

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Yutaka Takeuchi. 2024-10-31. Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces. https://arxiv.org/abs/2410.23859

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