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The Assouad dimension of randomly generated fractals

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dc.contributor.authorFraser, Jonathan MacDonald
dc.contributor.authorMiao, Jun Jie
dc.contributor.authorTroscheit, Sascha
dc.date.accessioned2017-03-23T00:33:18Z
dc.date.available2017-03-23T00:33:18Z
dc.date.issued2018-05
dc.identifier.citationFraser , J M , Miao , J J & Troscheit , S 2018 , ' The Assouad dimension of randomly generated fractals ' , Ergodic Theory and Dynamical Systems , vol. 38 , no. 3 , pp. 982-1011 . https://doi.org/10.1017/etds.2016.64en
dc.identifier.issn0143-3857
dc.identifier.otherPURE: 244093548
dc.identifier.otherPURE UUID: 1e68c2a3-123a-417e-96e5-0a7a7a4ab1c2
dc.identifier.otherScopus: 84988649457
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285492
dc.identifier.otherWOS: 000429684400008
dc.identifier.urihttps://hdl.handle.net/10023/10511
dc.descriptionJMF was financially supported by the EPSRC grant EP/J013560/1 whilst employed at the University of Warwick. JJM was partially supported by the NNSF of China (no. 11201152), the Fund for the Doctoral Program of Higher Education of China (no. 20120076120001) and SRF for ROCS, SEM (no. 01207427) ST was financially supported by the EPSRC Doctoral Training Grant EP/K503162/1.en
dc.description.abstractWe consider several dierent models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire typical Assouad dimension and consider some illustrative examples. Our results reveal a phenomenon common to each of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdor or packing dimension.
dc.language.isoeng
dc.relation.ispartofErgodic Theory and Dynamical Systemsen
dc.rights© Cambridge University Press, 2016. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.cambridge.org / http://dx.doi.org/10.1017/etds.2016.64en
dc.subjectAssouad dimensionen
dc.subjectRandom fractalen
dc.subjectSelf-similar seten
dc.subjectSelf-affine carpeten
dc.subjectMandelbrot percolationen
dc.subjectBaire categoryen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleThe Assouad dimension of randomly generated fractalsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/etds.2016.64
dc.description.statusPeer revieweden
dc.date.embargoedUntil2017-03-22


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