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arXiv · 1008.1147

The dimension of loop-erased random walk in 3D

David B. Wilson
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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.

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David B. Wilson. 2010-08-06. The dimension of loop-erased random walk in 3D. https://doi.org/10.1103/physreve.82.062102

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