Year: 2025
Type: preprint
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 $C\in(0,\infty)$.
Source: arXiv (Cornell University)
Authors: Cai, Gefei, Xie, Zhuoyan
Institution: Peking University
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417291965
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