Convergence in natural parametrization of random walk frontier
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912334347239424 |
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| author | Gao, Yifan Li, Xinyi Liu, Runsheng Liu, Xiangyi Shiraishi, Daisuke |
| author_facet | Gao, Yifan Li, Xinyi Liu, Runsheng Liu, Xiangyi Shiraishi, Daisuke |
| contents | In this paper, we show that the frontier of planar random walk converges weakly under natural parametrization to that of planar Brownian motion. As an intermediate result, we also show the convergence of the renormalized occupation measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence in natural parametrization of random walk frontier Gao, Yifan Li, Xinyi Liu, Runsheng Liu, Xiangyi Shiraishi, Daisuke Probability 82B41 (Primary) 60J65, 28A80 (Secondary) In this paper, we show that the frontier of planar random walk converges weakly under natural parametrization to that of planar Brownian motion. As an intermediate result, we also show the convergence of the renormalized occupation measure. |
| title | Convergence in natural parametrization of random walk frontier |
| topic | Probability 82B41 (Primary) 60J65, 28A80 (Secondary) |
| url | https://arxiv.org/abs/2504.13743 |