One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910075620163584 |
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| author | Bi, Yijie Gao, Yifan Li, Xinyi |
| author_facet | Bi, Yijie Gao, Yifan Li, Xinyi |
| contents | We study the one-arm probability in the level-set percolation of the discrete and metric-graph Gaussian free field (GFF) defined on a box with Dirichlet boundary conditions. For the metric-graph case, we establish asymptotic estimates on two one-arm probabilities of interest. For the discrete case, we show up-to-constants bounds on the point-to-bulk probability and demonstrate its difference from the metric-graph case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25400 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field Bi, Yijie Gao, Yifan Li, Xinyi Probability 60K35, 60G15, 60J45, 82B43 We study the one-arm probability in the level-set percolation of the discrete and metric-graph Gaussian free field (GFF) defined on a box with Dirichlet boundary conditions. For the metric-graph case, we establish asymptotic estimates on two one-arm probabilities of interest. For the discrete case, we show up-to-constants bounds on the point-to-bulk probability and demonstrate its difference from the metric-graph case. |
| title | One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field |
| topic | Probability 60K35, 60G15, 60J45, 82B43 |
| url | https://arxiv.org/abs/2603.25400 |