Dimension of the loop-erased random walk in three dimensions.

We measure the fractal dimension of loop-erased random walk (LERW) in three dimensions and estimate that it is 1.624 00 ± 0.000 05. 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.