Non-periodic systems with continuous diffraction measures
Abstract
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a `Palm-type' measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.
Cite
@article{arxiv.1502.05122,
title = {Non-periodic systems with continuous diffraction measures},
author = {Michael Baake and Matthias Birkner and Uwe Grimm},
journal= {arXiv preprint arXiv:1502.05122},
year = {2015}
}
Comments
31 pages, 4 figures; sections 1-5 are a review based on characteristic examples, while section 6 contains new material on the point process approach to diffraction