Non-existence of several random fractals in Brownian motion and Brownian loop soup
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913066415816704 |
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| author | Gao, Yifan Li, Xinyi Liu, Runsheng Qian, Wei |
| author_facet | Gao, Yifan Li, Xinyi Liu, Runsheng Qian, Wei |
| contents | We develop a unified approach to establish the non-existence of three types of random fractals: (1) the pioneer triple points of the planar Brownian motion, answering an open question in [7], (2) the pioneer double cut points of the planar and three-dimensional Brownian motions, and (3) the double points on the boundaries of the clusters of the planar Brownian loop soup at the critical intensity, answering an open question in [39]. These fractals have the common feature that they are associated with an intersection or disconnection exponent which yields a Hausdorff dimension ``exactly zero''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-existence of several random fractals in Brownian motion and Brownian loop soup Gao, Yifan Li, Xinyi Liu, Runsheng Qian, Wei Probability 60J65 (Primary) 28A80 (Secondary) We develop a unified approach to establish the non-existence of three types of random fractals: (1) the pioneer triple points of the planar Brownian motion, answering an open question in [7], (2) the pioneer double cut points of the planar and three-dimensional Brownian motions, and (3) the double points on the boundaries of the clusters of the planar Brownian loop soup at the critical intensity, answering an open question in [39]. These fractals have the common feature that they are associated with an intersection or disconnection exponent which yields a Hausdorff dimension ``exactly zero''. |
| title | Non-existence of several random fractals in Brownian motion and Brownian loop soup |
| topic | Probability 60J65 (Primary) 28A80 (Secondary) |
| url | https://arxiv.org/abs/2507.20324 |