The dimension of loop-erased random walk in 3D

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.

4 pages, 4 figures. v2 has more data, minor additional changes

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• Markov Chain Intersections and the Loop-Erased Walk
• Field theory conjecture for loop-erased random walks
• Scaling of loop-erased walks in 2 to 4 dimensions

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