An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk
Year: 2026
Type: preprint
Abstract: In this paper, we derive a new lower bound for the Hausdorff dimension of 3D Brownian cut points by proving an explicit upper bound ($<0.9999$) for $ξ_3(1,1)$, the intersection exponent for two independent Brownian motions in 3D. Consequently, the growth exponent of 3D loop-erased random walk is at least $1.0001$.
Source: arXiv (Cornell University)
Author: Liu, Runsheng
Institution: Peking University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213524188