Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914211273113600 |
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| author | Hernandez-Torres, Sarai Li, Xinyi Shiraishi, Daisuke |
| author_facet | Hernandez-Torres, Sarai Li, Xinyi Shiraishi, Daisuke |
| contents | In this work, we consider the scaling limit of loop-erased random walk (LERW) in three dimensions and prove that the limiting occupation measure is equivalent to its $β$-dimensional Minkowski content, where $β\in (1, 5/3]$ is its Hausdorff dimension. In doing this we also establish the existence of the two-point function and provide some sharp estimates on one-point function and ball-hitting probabilities for 3D LERW in any scale, which is a considerable improvement of previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk Hernandez-Torres, Sarai Li, Xinyi Shiraishi, Daisuke Probability 60K35, 82B41, 28A78 In this work, we consider the scaling limit of loop-erased random walk (LERW) in three dimensions and prove that the limiting occupation measure is equivalent to its $β$-dimensional Minkowski content, where $β\in (1, 5/3]$ is its Hausdorff dimension. In doing this we also establish the existence of the two-point function and provide some sharp estimates on one-point function and ball-hitting probabilities for 3D LERW in any scale, which is a considerable improvement of previous results. |
| title | Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk |
| topic | Probability 60K35, 82B41, 28A78 |
| url | https://arxiv.org/abs/2403.07256 |