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The Assouad spectrum of random self-affine carpets
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Troscheit, Sascha | |
dc.date.accessioned | 2021-04-14T23:50:12Z | |
dc.date.available | 2021-04-14T23:50:12Z | |
dc.date.issued | 2020-10-15 | |
dc.identifier | 269404977 | |
dc.identifier | 99f04307-3bf8-4450-bf21-ae8de2f415d4 | |
dc.identifier | 85093916070 | |
dc.identifier | 000692794800005 | |
dc.identifier.citation | Fraser , J & Troscheit , S 2020 , ' The Assouad spectrum of random self-affine carpets ' , Ergodic Theory and Dynamical Systems , vol. First View . https://doi.org/10.1017/etds.2020.93 | en |
dc.identifier.issn | 0143-3857 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/83481811 | |
dc.identifier.uri | https://hdl.handle.net/10023/23032 | |
dc.description | Funding: JMF was financially supported by the Leverhulme Trust Research Fellowship RF-2016-500, the EPSRC Standard Grant EP/R015104/1, and the University of Waterloo. ST was financially supported by NSERC Grants 2014-03154 and 2016-03719, and the University of Waterloo. | en |
dc.description.abstract | We derive the almost sure Assouad spectrum and quasi-Assouad dimension of one-variable random self-affine Bedford–McMullen carpets. Previous work has revealed that the (related) Assouad dimension is not sufficiently sensitive to distinguish between subtle changes in the random model, since it tends to be almost surely ‘as large as possible’ (a deterministic quantity). This has been verified in conformal and non-conformal settings. In the conformal setting, the Assouad spectrum and quasi-Assouad dimension behave rather differently, tending to almost surely coincide with the upper box dimension. Here we investigate the non-conformal setting and find that the Assouad spectrum and quasi-Assouad dimension generally do not coincide with the box dimension or Assouad dimension. We provide examples highlighting the subtle differences between these notions. Our proofs combine deterministic covering techniques with suitably adapted Chernoff estimates and Borel–Cantelli-type arguments. | |
dc.format.extent | 19 | |
dc.format.extent | 456906 | |
dc.language.iso | eng | |
dc.relation.ispartof | Ergodic Theory and Dynamical Systems | en |
dc.subject | Assouad spectrum | en |
dc.subject | Quasi-Assouad dimension | en |
dc.subject | Random self-affine carpet | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | The Assouad spectrum of random self-affine carpets | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1017/etds.2020.93 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2021-04-15 | |
dc.identifier.grantnumber | RF-2016-500 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
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