dc.contributor.author Hermon, Jonathan dc.contributor.author Hutchcroft, Tom dc.date.accessioned 2021-10-22T15:50:27Z dc.date.available 2021-10-22T15:50:27Z dc.date.issued 2020-10-22 dc.date.submitted 2019-05-10 dc.identifier.issn 0020-9910 dc.identifier.other s00222-020-01011-3 dc.identifier.other 1011 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/329768 dc.description Funder: University of Cambridge dc.description.abstract Abstract: Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and p>pc(G) then there exists a positive constant cp such that Pp(n≤|K|<∞)≤e-cpnfor every n≥1, where K is the cluster of the origin. We deduce the following two corollaries: Every infinite cluster in supercritical percolation on a transitive nonamenable graph has anchored expansion almost surely. This answers positively a question of Benjamini et al. (in: Random walks and discrete potential theory (Cortona, 1997), symposium on mathematics, XXXIX, Cambridge University Press, Cambridge, pp 56–84, 1999). For transitive nonamenable graphs, various observables including the percolation probability, the truncated susceptibility, and the truncated two-point function are analytic functions of p throughout the supercritical phase. dc.language en dc.publisher Springer Berlin Heidelberg dc.subject Article dc.title Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution dc.type Article dc.date.updated 2021-10-22T15:50:26Z prism.endingPage 486 prism.issueIdentifier 2 prism.publicationName Inventiones mathematicae prism.startingPage 445 prism.volume 224 dc.identifier.doi 10.17863/CAM.77213 dcterms.dateAccepted 2020-10-13 rioxxterms.versionofrecord 10.1007/s00222-020-01011-3 rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.identifier.eissn 1432-1297
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