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Exact dimensionality and projection properties of Gaussian multiplicative chaos measures
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dc.contributor.author | Falconer, Kenneth | |
dc.contributor.author | Jin, Xiong | |
dc.date.accessioned | 2018-12-14T11:30:04Z | |
dc.date.available | 2018-12-14T11:30:04Z | |
dc.date.issued | 2019-08-15 | |
dc.identifier | 240125030 | |
dc.identifier | db68a015-9c96-4953-a343-9278a888ee1d | |
dc.identifier | 85075129461 | |
dc.identifier | 000478938400023 | |
dc.identifier.citation | Falconer , 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/7776 | en |
dc.identifier.issn | 0002-9947 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1601.00556v1 | |
dc.identifier.other | ORCID: /0000-0001-8823-0406/work/58055270 | |
dc.identifier.uri | https://hdl.handle.net/10023/16688 | |
dc.description | Paper originally entitled 'Hölder continuity of the Liouville Quantum Gravity measure' | en |
dc.description.abstract | Given 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.extent | 37 | |
dc.format.extent | 492074 | |
dc.language.iso | eng | |
dc.relation.ispartof | Transactions of the American Mathematical Society | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | Exact dimensionality and projection properties of Gaussian multiplicative chaos measures | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1090/tran/7776 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2019-07776-0/ | en |
dc.identifier.url | http://arxiv.org/abs/1601.00556 | en |
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