Percolation of fat Poisson cylinders in hyperbolic space
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909439352635392 |
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| author | Betken, Carina Broman, Erik Gusakova, Anna Thäle, Christoph |
| author_facet | Betken, Carina Broman, Erik Gusakova, Anna Thäle, Christoph |
| contents | In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We prove this by establishing a novel link between the fat Poisson cylinder process and semi-scale invariant random fractal models on the unit sphere and in $\mathbb{R}^d.$ As a secondary result, we show that the semi-scale invariant fractal ball model in $\mathbb{R}^d$ has a non-empty sheet phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Percolation of fat Poisson cylinders in hyperbolic space Betken, Carina Broman, Erik Gusakova, Anna Thäle, Christoph Probability In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We prove this by establishing a novel link between the fat Poisson cylinder process and semi-scale invariant random fractal models on the unit sphere and in $\mathbb{R}^d.$ As a secondary result, we show that the semi-scale invariant fractal ball model in $\mathbb{R}^d$ has a non-empty sheet phase. |
| title | Percolation of fat Poisson cylinders in hyperbolic space |
| topic | Probability |
| url | https://arxiv.org/abs/2412.17757 |