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Uniform Distribution in Model Sets

Published online by Cambridge University Press:  20 November 2018

Robert V. Moody
Robert V. Moody*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1
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Abstract

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We give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the ‘physical’) space and its internal space. We prove, assuming only that the window defining the model set is measurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive.

Keywords

52C2311K7028D0537A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 123 - 130
Copyright
Copyright © Canadian Mathematical Society 2002

References

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