Canadian Mathematical Bulletin· 2026Q2
Model sets with precompact Borel windows
- 2citations
- Q2SCImago
- 2026year
Short summary
Almost surely, point sets generated by precompact Borel windows in a cut and project scheme result in pure point diffractive sets with specific autocorrelation and diffraction patterns.
AI-generated from the title and abstract; the full text is not read.
Key points
- Point sets from precompact Borel windows in cut and project schemes are almost surely Besicovitch almost periodic Dirac combs.
- These sets are pure point diffractive, with autocorrelation defined by the window's covariogram.
- Diffraction patterns are the inverse Fourier transform of the window squared.
- Bragg peak intensities are determined by the absolute value squared of Fourier–Bohr coefficients.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Given a cut and project scheme and a precompact Borel window, we show that almost surely all positions of the window give rise to point sets with Besicovitch almost periodic Dirac combs. In particular, all those positions lead to pure point diffractive point sets with autocorrelation given by the covariogram of the window and diffraction given by the inverse Fourier transform of the window squared. Moreover, the Fourier–Bohr coefficients exist and the intensity of the Bragg peaks is given by their absolute value squared. We show the existence of an ergodic measure with pure point dynamical spectrum such that all those window positions give rise to point sets which are generic for this measure.
The authors' abstract, as published at the source. Canadian Mathematical Bulletin, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Materials Chemistry
Materials ChemistryMaterials Science