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• W3034894071 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 (Probability on Trees and Networks (2016) Cambridge Univ. Press) in the negative. A version of our argument gives an example of a nonunimodular transitive graph where WUSF≠FUSF, but some of the FUSF trees are light with respect to Haar measure. This disproves a conjecture of Tang (Electron. J. Probab. 26 (2021) Paper No. 141)." @default.
• W3034894071 created "2020-06-19" @default.
• W3034894071 creator A5032061087 @default.
• W3034894071 creator A5063213545 @default.
• W3034894071 date "2022-11-01" @default.
• W3034894071 modified "2023-09-26" @default.
• W3034894071 title "The Free Uniform Spanning Forest is disconnected in some virtually free groups, depending on the generator set" @default.
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• W3034894071 doi "https://doi.org/10.1214/22-aop1581" @default.
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