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dc.contributor.authorBreuillard, Emmanuel
dc.contributor.authorVarjú, PP
dc.date.accessioned2019-01-11T00:31:21Z
dc.date.available2019-01-11T00:31:21Z
dc.date.issued2020-03
dc.identifier.issn0021-7670
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/287816
dc.description.abstractThe exponential growth rate of non polynomially growing subgroups of $GL_d$ is conjectured to admit a uniform lower bound. This is known for non-amenable subgroups, while for amenable subgroups it is known to imply the Lehmer conjecture from number theory. In this note, we show that it is equivalent to the Lehmer conjecture. This is done by establishing a lower bound for the entropy of the random walk on the semigroup generated by the maps $x\mapsto \lambda\cdot x\pm 1$, where $\lambda$ is an algebraic number. We give a bound in terms of the Mahler measure of $\lambda$. We also derive a bound on the dimension of Bernoulli convolutions.
dc.description.sponsorshipSimons Foundation Royal Society ERC
dc.publisherSpringer Science and Business Media LLC
dc.titleEntropy of Bernoulli convolutions and uniform exponential growth for linear groups
dc.typeArticle
prism.endingPage481
prism.issueIdentifier2
prism.publicationDate2020
prism.publicationNameJournal d'Analyse Mathematique
prism.startingPage443
prism.volume140
dc.identifier.doi10.17863/CAM.35131
dcterms.dateAccepted2018-06-10
rioxxterms.versionofrecord10.1007/s11854-020-0100-0
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2020-03-01
dc.identifier.eissn1565-8538
rioxxterms.typeJournal Article/Review
pubs.funder-project-idRoyal Society (UF140146)
pubs.funder-project-idSimons Foundation (LETTER DATED 10-NOV-09)
cam.issuedOnline2020-04-20
cam.orpheus.successTue May 26 08:17:26 BST 2020 - Embargo updated
cam.orpheus.counter9
rioxxterms.freetoread.startdate2021-03-01


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