One-arm exponents of high-dimensional percolation revisited
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912669074718720 |
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| author | van Engelenburg, Diederik Garban, Christophe Panis, Romain Severo, Franco |
| author_facet | van Engelenburg, Diederik Garban, Christophe Panis, Romain Severo, Franco |
| contents | We consider sufficiently spread-out Bernoulli percolation in dimensions ${d>6}$. We present a short and simple proof of the up-to-constants estimate for the one-arm probability in both the full-space and half-space settings. These results were previously established by Kozma and Nachmias and by Chatterjee and Hanson, respectively. Our proof improves upon the entropic technique introduced by Dewan and Muirhead, relying on a sharp estimate on a suitably chosen correlation length recently obtained by Duminil-Copin and Panis. This approach is inspired by our companion work, where we compute the one-arm exponent for several percolation models related to the high-dimensional Ising model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-arm exponents of high-dimensional percolation revisited van Engelenburg, Diederik Garban, Christophe Panis, Romain Severo, Franco Probability Mathematical Physics 60K35, 82B20, 82B27, 82B43 We consider sufficiently spread-out Bernoulli percolation in dimensions ${d>6}$. We present a short and simple proof of the up-to-constants estimate for the one-arm probability in both the full-space and half-space settings. These results were previously established by Kozma and Nachmias and by Chatterjee and Hanson, respectively. Our proof improves upon the entropic technique introduced by Dewan and Muirhead, relying on a sharp estimate on a suitably chosen correlation length recently obtained by Duminil-Copin and Panis. This approach is inspired by our companion work, where we compute the one-arm exponent for several percolation models related to the high-dimensional Ising model. |
| title | One-arm exponents of high-dimensional percolation revisited |
| topic | Probability Mathematical Physics 60K35, 82B20, 82B27, 82B43 |
| url | https://arxiv.org/abs/2510.21595 |