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The dimension of loop-erased random walk in 3D

· 2010 · cond-mat.stat-mech · arXiv 1008.1147

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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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cond-mat.stat-mech 1

years

2026 1

verdicts

UNVERDICTED 1

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Field theories for Laplacian Growth

cond-mat.stat-mech · 2026-06-25 · unverdicted · novelty 7.0

Constructs exact lattice action for LRWs with perturbative equivalence to LERWs and generalizes to b-LRWs and DLA.

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  • Field theories for Laplacian Growth cond-mat.stat-mech · 2026-06-25 · unverdicted · none · ref 5 · internal anchor

    Constructs exact lattice action for LRWs with perturbative equivalence to LERWs and generalizes to b-LRWs and DLA.