Diffraction of compatible random substitutions in one dimension
diffraction, Fibonacci substitutions, Kronecker factor
As 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.
Baake, M., Spindeler, T., & Strungaru, N. (2018). Diffraction of compatible random substitutions in one dimension. arXiv:1712.00323v2. https://arxiv.org/abs/1712.00323
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