The dimension of loop-erased random walk in 3D
Statistical Mechanics
2012-06-26 v2
Abstract
We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.
Keywords
Cite
@article{arxiv.1008.1147,
title = {The dimension of loop-erased random walk in 3D},
author = {David B. Wilson},
journal= {arXiv preprint arXiv:1008.1147},
year = {2012}
}
Comments
4 pages, 4 figures. v2 has more data, minor additional changes