The dimension of loop-erased random walk in 3D

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.