Backbone probability of planar Brownian motion
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917240373248000 |
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| author | Cai, Gefei Xie, Zhuoyan |
| author_facet | Cai, Gefei Xie, Zhuoyan |
| contents | Motivated by critical planar percolation, we investigate a ``backbone'' event of planar Brownian motion, i.e.~the existence of two disjoint subpaths on the Brownian trajectory connecting the $\varepsilon$-neighborhood of the starting point to a macroscopic distance. We show that the probability of this event is $C(\log|\log\varepsilon|)^{-1}(1+o(1))$ as $\varepsilon\to0$ for some constant $C\in(0,\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backbone probability of planar Brownian motion Cai, Gefei Xie, Zhuoyan Probability Mathematical Physics 60J65, 60J67 Motivated by critical planar percolation, we investigate a ``backbone'' event of planar Brownian motion, i.e.~the existence of two disjoint subpaths on the Brownian trajectory connecting the $\varepsilon$-neighborhood of the starting point to a macroscopic distance. We show that the probability of this event is $C(\log|\log\varepsilon|)^{-1}(1+o(1))$ as $\varepsilon\to0$ for some constant $C\in(0,\infty)$. |
| title | Backbone probability of planar Brownian motion |
| topic | Probability Mathematical Physics 60J65, 60J67 |
| url | https://arxiv.org/abs/2512.09683 |