Diffraction of compatible random substitutions in one dimension

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dc.contributor.authorBaake, Michael
dc.contributor.authorSpindeler, Timo
dc.contributor.authorStrungaru, Nicolae
dc.date.accessioned2021-01-15
dc.date.accessioned2022-05-31T01:43:06Z
dc.date.available2022-05-31T01:43:06Z
dc.date.issued2018
dc.description.abstractAs a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our revised approach yields explicit formulas for the pure point and the absolutely continuous parts, as well as a proof for the absence of singular continuous components. This approach is then extended to the family of random noble means substitutions and, as an example with an underlying 2-adic structure, to a locally randomised version of the period doubling chain. As a first step towards a more general approach, we interpret our findings in terms of a disintegration over the Kronecker factor, which is the maximal equicontinuous factor of a covering model set.
dc.format.extent488.63KB
dc.format.mimetypePDF
dc.identifier.citationBaake, M., Spindeler, T., & Strungaru, N. (2018). Diffraction of compatible random substitutions in one dimension. arXiv:1712.00323v2. https://arxiv.org/abs/1712.00323
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2134
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjectdiffraction
dc.subjectFibonacci substitutions
dc.subjectKronecker factor
dc.titleDiffraction of compatible random substitutions in one dimension
dc.typeReport
dspace.entity.type
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