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An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk
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 ξ3(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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BibTeX
@misc{liu2026explicit,
title = {{An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk}},
author = {Runsheng Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18643},
eprint = {2609.18643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18643},
}
RIS
TY - UNPB
TI - An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk
AU - Runsheng Liu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18643
UR - https://arxiv.org/abs/2609.18643
AB - 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 $1.0001$.
ER -