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Statistics of patterns in typical cut and project sets

Published online by Cambridge University Press:  13 March 2018

ALAN HAYNES ,
ANTOINE JULIEN ,
HENNA KOIVUSALO  and
JAMES WALTON
ALAN HAYNES
Affiliation:
Department of Mathematics, University of Houston, Philip Guthrie Hoffman Hall, 3551 Cullen Blvd., Room 641, Houston, TX 77204-3008, USA email [email protected]
ANTOINE JULIEN
Affiliation:
Nord universitet, Levanger Røstad, Høgskoleveien 27, 7600 Levanger, Norway email [email protected]
HENNA KOIVUSALO
Affiliation:
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-platz 1, 1090 Vienna, Austria email [email protected]
JAMES WALTON
Affiliation:
Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, UK email [email protected]
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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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 12 , December 2019 , pp. 3365 - 3387
Copyright
© Cambridge University Press, 2018 

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