On weak model sets of extremal density
By Michael Baake, Christian Huck, Nicolae Strungaru. 2015
54 citations recorded by the source corpus.
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a boundary of positive measure, or even consists of boundary only. The latter phenomena are related to the topological entropy of the corresponding dynamical system and to various other unusual properties. Under a rather natural extremality assumption on the density of the weak model set we establish its pure point diffraction nature. We derive an explicit formula that can be seen as the generalisation of the case of regular model sets. Furthermore, the corresponding natural patch frequency measure is shown to be ergodic. Since weak model sets of extremal density are generic for this measure, one obtains that the dynamical spectrum of the hull is pure point as well.
Subfields: Materials Chemistry, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0181098dbdaec9e6a81aee0cacabdca08120e8e1
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In Materials Chemistry
In Mathematical Physics
Citations in the corpus
- Dynamics on the graph of the torus parametrization (2015, methodology): “Compare the approach by Baake and Moody [8], which is based on the autocorrelation of the point set, and which has recently been revisited by Strungaru [59].”
- Sarnak’s Conjecture: What’s New (2017, unknown): “Finally, for a generalization to so-called weak model sets, see [15], and for some results related to the distribution of B-free integers, see [10, 11].”