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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02881 |
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| _version_ | 1866916552316551168 |
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| author | Peretz, Tal |
| author_facet | Peretz, Tal |
| contents | We consider the Gaussian free field $φ$ on $\mathbb{Z}^d$ for $d \geq 3$ and study the level sets $\{φ\geq h \}$ in the percolating regime. We prove upper and lower bounds for the probability that the chemical distance is much larger than Euclidean distance. Our proof uses a renormalization scheme combined with a bootstrap argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chemical Distance for the Level Sets of the Gaussian Free Field Peretz, Tal Probability 60K35, 82B43 We consider the Gaussian free field $φ$ on $\mathbb{Z}^d$ for $d \geq 3$ and study the level sets $\{φ\geq h \}$ in the percolating regime. We prove upper and lower bounds for the probability that the chemical distance is much larger than Euclidean distance. Our proof uses a renormalization scheme combined with a bootstrap argument. |
| title | Chemical Distance for the Level Sets of the Gaussian Free Field |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2501.02881 |