Statistics of patterns in typical cut and project sets. (English) Zbl 1448.37010
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.
MSC:
| 37A50 | Dynamical systems and their relations with probability theory and stochastic processes |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 37B10 | Symbolic dynamics |
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