PAIR CORRELATIONS OF ONE-DIMENSIONAL MODEL SETS AND MONSTROUS COVARIOGRAMS OF RAUZY FRACTALS
Abstract
Abstract The averaged distance structure of one-dimensional regular model sets is determined via their pair-correlation functions. The latter lead to covariograms and cross covariograms of the windows, which give continuous functions in internal space. While they are simple tent-shaped, piecewise linear functions for intervals, the typical case for inflation systems leads to convolutions of Rauzy fractals, which are difficult to compute. In the presence of an inflation structure, an alternative path is possible via the exact renormalisation structures of the pair-correlation functions. We introduce this approach and derive two concrete examples, which display unexpectedly complex and wild behaviour.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Statistical Mechanics and Entropy
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Journal of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 120
- Issue
- 3
- Pages
- 305–324
- Publication date
- 10 March 2026
- Language
- EN