The Free Uniform Spanning Forest is disconnected in some virtually free groups, depending on the generator set
نویسندگان
چکیده
We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such Free Uniform Spanning Forest in direct product of k-regular tree has infinitely many trees almost surely. This shows number FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley same virtually free group one, but connected other, answering question Lyons Peres (Probability on Trees Networks (2016) Cambridge Univ. Press) negative. A version our argument gives an example nonunimodular graph where WUSF≠FUSF, some are light with respect to Haar measure. disproves conjecture Tang (Electron. J. Probab. 26 (2021) Paper No. 141).
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ژورنال
عنوان ژورنال: Annals of Probability
سال: 2022
ISSN: ['0091-1798', '2168-894X']
DOI: https://doi.org/10.1214/22-aop1581