Supercritical sharpness for Voronoi percolation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912084281786368 |
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| author | Dembin, Barbara Severo, Franco |
| author_facet | Dembin, Barbara Severo, Franco |
| contents | We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett & Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques used to study several fine properties of the supercritical phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00555 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Supercritical sharpness for Voronoi percolation Dembin, Barbara Severo, Franco Probability Mathematical Physics 82B43, 60K35 We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett & Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques used to study several fine properties of the supercritical phase. |
| title | Supercritical sharpness for Voronoi percolation |
| topic | Probability Mathematical Physics 82B43, 60K35 |
| url | https://arxiv.org/abs/2311.00555 |