Statistics of patterns in typical cut and project sets

In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in...

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Published in:Ergodic theory and dynamical systems 2019-12, Vol.39 (12), p.3365-3387
Main Authors: HAYNES, ALAN, JULIEN, ANTOINE, KOIVUSALO, HENNA, WALTON, JAMES
Format: Article
Language:English
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Summary:In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in discrepancy theory.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2018.15