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dc.contributor.authorHermon, Jonathan
dc.contributor.authorHutchcroft, Tom
dc.date.accessioned2021-10-22T15:50:27Z
dc.date.available2021-10-22T15:50:27Z
dc.date.issued2020-10-22
dc.date.submitted2019-05-10
dc.identifier.issn0020-9910
dc.identifier.others00222-020-01011-3
dc.identifier.other1011
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/329768
dc.descriptionFunder: University of Cambridge
dc.description.abstractAbstract: 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.languageen
dc.publisherSpringer Berlin Heidelberg
dc.subjectArticle
dc.titleSupercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution
dc.typeArticle
dc.date.updated2021-10-22T15:50:26Z
prism.endingPage486
prism.issueIdentifier2
prism.publicationNameInventiones mathematicae
prism.startingPage445
prism.volume224
dc.identifier.doi10.17863/CAM.77213
dcterms.dateAccepted2020-10-13
rioxxterms.versionofrecord10.1007/s00222-020-01011-3
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1432-1297


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