Statistics of patterns in typical cut and project sets

Haynes, Alan; Julien, Antoine; Koivusalo, Henna; Walton, James

doi:10.1017/etds.2018.15

Statistics of patterns in typical cut and project sets

Haynes, Alan; Julien, Antoine; Koivusalo, Henna; Walton, James

Authors

Alan Haynes

Antoine Julien

Henna Koivusalo

James Walton

Abstract

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.

Citation

Haynes, A., Julien, A., Koivusalo, H., & Walton, J. (2019). Statistics of patterns in typical cut and project sets. Ergodic Theory and Dynamical Systems, 39(12), 3365-3387. https://doi.org/10.1017/etds.2018.15

Journal Article Type	Article
Acceptance Date	Aug 29, 2017
Online Publication Date	Mar 13, 2018
Publication Date	Dec 31, 2019
Deposit Date	Feb 21, 2017
Publicly Available Date	Apr 4, 2018
Journal	Ergodic Theory and Dynamical Systems
Print ISSN	0143-3857
Electronic ISSN	1469-4417
Publisher	Cambridge University Press
Peer Reviewed	Peer Reviewed
Volume	39
Issue	12
Pages	3365-3387
DOI	https://doi.org/10.1017/etds.2018.15
Related Public URLs	https://arxiv.org/abs/1702.04041

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Copyright Statement
This article has been published in a revised form in Ergodic theory and dynamical systems https://doi.org/10.1017/etds.2018.15. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press, 2018.