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dc.contributor.authorHuveneers, François
dc.date.accessioned2012-06-13T16:30:47Z
dc.date.available2012-06-13T16:30:47Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9455
dc.language.isoenen
dc.subjectAsymptotesen
dc.subjectMeasure theoryen
dc.subject.ddc519en
dc.titleSubdiffusive behavior generated by irrational rotationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study asymptotic distributions of the sums yn(x)=∑ k=0n−1ψ(x+kα) with respect to the Lebesgue measure, where αxs2208xs211D−xs211A and where ψ is the 1-periodic function of bounded variation such that ψ(x)=1 if xxs2208[0,1/2[ and ψ(x)=−1 if xxs2208[1/2,1[. For every αxs2208xs211D−xs211A, we find a sequence (nj)jxs2282xs2115 such that $y_{n_j}/\sqrt j$ is asymptotically normally distributed. For n≥1, let znxs2208(ym)m≤n be such that xs2016znxs2016L2=max m≤nxs2016ymxs2016L2. If α is of constant type, we show that zn/xs2016znxs2016L2 is also asymptotically normally distributed. We give a heuristic link with the theory of expanding maps of the interval.en
dc.relation.isversionofjnlnameErgodic Theory and Dynamical Systems
dc.relation.isversionofjnlvol29en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages1217-1233en
dc.relation.isversionofdoihttp://dx.doi.org/10.1017/S0143385708000680en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00701757en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherCambridge University Pressen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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