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arXiv · 2512.09683

Backbone probability of planar Brownian motion

Gefei Cai·Zhuoyan Xie
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Abstract

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 $C\in(0,\infty)$.

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Gefei Cai, Zhuoyan Xie. 2025-12-10. Backbone probability of planar Brownian motion. https://arxiv.org/abs/2512.09683

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