Indistinguishability of Percolation Clusters

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dc.creatorLyons, Russell
dc.creatorSchramm, Oded
dc.date1998-11-29
dc.date1999-05-02
dc.date.accessioned2026-07-07T10:22:31Z
dc.date.available2026-07-07T10:22:31Z
dc.descriptionWe show that when percolation produces infinitely many infinite clusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property. This implies that uniqueness of the infinite cluster is equivalent to non-decay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products, and inequalities for $p_u$.
dc.descriptionTo appear in Ann. Probab
dc.identifierhttps://arxiv.org/abs/math/9811170
dc.identifierhttp://arxiv.org/abs/math/9811170
dc.identifierAnnalsProbab.27:1809-1836,1999
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/175540
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject82B43, 60B99 (Primary), 60K35, 60D05 (Secondary)
dc.titleIndistinguishability of Percolation Clusters
dc.typetext

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