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arXiv · 2609.18643

An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk

Runsheng Liu
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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 $1.0001$.

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Runsheng Liu. 2026-09-16. An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk. https://arxiv.org/abs/2609.18643

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