Nonamenable products are not treeable
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Publication:1580502
DOI10.1007/BF02803520zbMATH Open0961.43002arXivmath/0404096MaRDI QIDQ1580502
Author name not available (Why is that?)
Publication date: 20 May 2001
Published in: (Search for Journal in Brave)
Abstract: Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product, has infinitely many connected components almost surely.
Full work available at URL: https://arxiv.org/abs/math/0404096
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