Indistinguishability of the components of random spanning forests
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Publication:1660632
DOI10.1214/17-AOP1225zbMATH Open1430.60020arXiv1506.01370MaRDI QIDQ1660632
Author name not available (Why is that?)
Publication date: 16 August 2018
Published in: (Search for Journal in Brave)
Abstract: We prove that the infinite components of the Free Uniform Spanning Forest of a Cayley graph are indistinguishable by any invariant property, given that the forest is different from its wired counterpart. Similar result is obtained for the Free Minimal Spanning Forest. We also show that with the above assumptions there can only be 0, 1 or infinitely many components. These answer questions by Benjamini, Lyons, Peres and Schramm. Our methods apply to a more general class of percolations, those satisfying "weak insertion tolerance", and work beyond Cayley graphs, in the more general setting of unimodular random graphs.
Full work available at URL: https://arxiv.org/abs/1506.01370
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