Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Choosing a Spanning Tree for the Integer Lattice Uniformly   Consider the nearest neighbor graph for the integer lattice Z^d in d
dimensions. For a large finite piece of it, consider choosing a spanning tree
for that piece uniformly among all possible subgraphs that are spanning trees.
As the piece gets larger, this approaches a limiting measure on the set of
spanning graphs for Z^d. This is shown to be a tree if and only if d=<4. In
this case, the tree has only one topological end, i.e. there are no doubly
infinite paths. When d>=5 the spanning forest has infinitely many components
almost surely, with each component having one or two topological ends.

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The categories of this paper are: stat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an