Non-amenable products are not treeable

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dc.creatorPemantle, Robin
dc.creatorPeres, Yuval
dc.date2004-04-05
dc.date.accessioned2026-07-07T05:07:08Z
dc.date.available2026-07-07T05:07:08Z
dc.descriptionLet 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0404096
dc.identifierhttp://arxiv.org/abs/math/0404096
dc.identifierIsrael J. Math, 118, 147-155 (2000)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70743
dc.subjectProbability
dc.subjectGeometric Topology
dc.subject60B99 (Primary) 60D05, 20F32 (Secondary)
dc.titleNon-amenable products are not treeable
dc.typetext

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