Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917824764575744 |
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| author | Takeuchi, Yutaka |
| author_facet | Takeuchi, Yutaka |
| contents | 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, Gouéré 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 Gouéré's result to Ahlfors regular metric measure spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces Takeuchi, Yutaka Probability Metric Geometry 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, Gouéré 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 Gouéré's result to Ahlfors regular metric measure spaces. |
| title | Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces |
| topic | Probability Metric Geometry |
| url | https://arxiv.org/abs/2410.23859 |