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dc.contributor.authorFalconer, Kenneth
dc.contributor.authorJin, Xiong
dc.date.accessioned2018-12-14T11:30:04Z
dc.date.available2018-12-14T11:30:04Z
dc.date.issued2019-08-15
dc.identifier240125030
dc.identifierdb68a015-9c96-4953-a343-9278a888ee1d
dc.identifier85075129461
dc.identifier000478938400023
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 . https://doi.org/10.1090/tran/7776en
dc.identifier.issn0002-9947
dc.identifier.otherArXiv: http://arxiv.org/abs/1601.00556v1
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055270
dc.identifier.urihttps://hdl.handle.net/10023/16688
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.format.extent37
dc.format.extent492074
dc.language.isoeng
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleExact dimensionality and projection properties of Gaussian multiplicative chaos measuresen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1090/tran/7776
dc.description.statusPeer revieweden
dc.identifier.urlhttps://www.ams.org/journals/tran/0000-000-00/S0002-9947-2019-07776-0/en
dc.identifier.urlhttp://arxiv.org/abs/1601.00556en


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