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- W4307191833 abstract "We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely. This shows that the number of trees in the FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley graphs of the same virtually free group such that the FUSF has infinitely many trees in one, but is connected in the other, answering a question of Lyons and Peres (2016) in the negative. A version of our argument gives an example of a non-unimodular transitive graph where WUSFnot=FUSF, but some of the FUSF trees are light with respect to Haar measure. This disproves a conjecture of Tang (2019)." @default.
- W4307191833 created "2022-10-29" @default.
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- W4307191833 date "2020-06-11" @default.
- W4307191833 modified "2023-09-24" @default.
- W4307191833 title "The Free Uniform Spanning Forest is disconnected in some virtually free groups, depending on the generator set" @default.
- W4307191833 doi "https://doi.org/10.48550/arxiv.2006.06387" @default.
- W4307191833 hasPublicationYear "2020" @default.
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