Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int