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The dimension of loop-erased random walk in 3D

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arxiv 1008.1147 v2 pith:SU344C2A submitted 2010-08-06 cond-mat.stat-mech

David B. Wilson This is my paper · ORCID
classification cond-mat.stat-mech
keywords cubiclerwdimensionface-centeredloop-erasedrandomwalkabelian
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Field theories for Laplacian Growth

    cond-mat.stat-mech 2026-06 unverdicted novelty 7.0 of 10

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

  2. Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models

    cond-mat.stat-mech 2019-08 accept novelty 7.0 of 10

    A six-loop field-theoretic calculation gives the fractal dimension of critical curves and the crossover exponent in O(n) models, with estimates for LERW, SAW, Ising, XY and Heisenberg systems.

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