Ends in Uniform Spanning Forests

Mathematics – Probability

Scientific paper

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22 pages

Scientific paper

It has hitherto been known that in a transitive unimodular graph, each tree
in the wired spanning forest has only one end a.s. We dispense with the
assumptions of transitivity and unimodularity, replacing them with a much
broader condition on the isoperimetric profile that requires just slightly more
than uniform transience.

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