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dc.contributor.authorBreuillard, Emmanuelen
dc.contributor.authorVarjú, PPen
dc.date.accessioned2019-10-11T23:30:53Z
dc.date.available2019-10-11T23:30:53Z
dc.identifier.issn0091-1798
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/297783
dc.description.abstractThe Bernoulli convolution with parameter λ ∈ (0, 1) is the probability measure μλ that is the law of the random variable σn ≥ 0 ±λn, where the signs are independent unbiased coin tosses. We prove that each parameter λ ∈ (1/2, 1) with dimμλ < 1 can be approximated by algebraic parameters η ∈ (1/2, 1) within an error of order exp(-deg(η)A) such that dimμη < 1, for any number A. As a corollary, we conclude that dimμλ = 1 for each of λ = ln 2, e-1/2,π/4. These are the first explicit examples of such transcendental parameters. Moreover, we show that Lehmer's conjecture implies the existence of a constant a < 1 such that dimμλ = 1 for all λ ∈ (a, 1).
dc.publisherInstitute of Mathematical Statistics
dc.rightsAll rights reserved
dc.titleOn the dimension of Bernoulli convolutionsen
dc.typeArticle
prism.endingPage2617
prism.issueIdentifier4en
prism.publicationNameAnnals of Probabilityen
prism.startingPage2582
prism.volume47en
dc.identifier.doi10.17863/CAM.44836
rioxxterms.versionofrecord10.1214/18-AOP1324en
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
dc.identifier.eissn2168-894X
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idRoyal Society (UF140146)
cam.issuedOnline2019-07-04en


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