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dc.contributor.authorFalconer, Kenneth
dc.contributor.authorJin, Xiong
dc.identifier.citationFalconer , K & Jin , X 2019 , ' Exact dimensionality and projection properties of Gaussian multiplicative chaos measures ' , Transactions of the American Mathematical Society , vol. 372 , no. 4 , pp. 2921-2957 .
dc.identifier.otherPURE: 240125030
dc.identifier.otherPURE UUID: db68a015-9c96-4953-a343-9278a888ee1d
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055270
dc.identifier.otherScopus: 85075129461
dc.descriptionPaper originally entitled 'Hölder continuity of the Liouville Quantum Gravity measure'en
dc.description.abstractGiven a measure ν on a regular planar domain D, the Gaussian multiplicative chaos measure of ν studied in this paper is the random measure ^ν^ obtained as the limit of the exponential of the γ-parameter circle averages of the Gaussian free field on D weighted by ν. We investigate the dimensional and geometric properties of these random measures. We first show that if ν is a finite Borel measure on D with exact dimension α>0, then the associated GMC measure ^ν^ is nondegenerate and is almost surely exact dimensional with dimension α-γ2/2, provided γ2/2<α. We then show that if νt is a Hölder-continuously parameterized family of measures, then the total mass of ^νt^ varies Hölder-continuously with t, provided that γ is sufficiently small. As an application we show that if γ<0.28, then, almost surely, the orthogonal projections of the γ-Liouville quantum gravity measure ^ν^ on a rotund convex domain D in all directions are simultaneously absolutely continuous with respect to Lebesgue measure with Hölder continuous densities. Furthermore, ^ν^ has positive Fourier dimension almost surely.
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.rightsCopyright © 2018, American Mathematical Society. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectQA Mathematicsen
dc.titleExact dimensionality and projection properties of Gaussian multiplicative chaos measuresen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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