Geodesic
Uniform Distribution in Model Sets
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 123-130

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2002-015-3
Mots-clés : 52C23, 11K70, 28D05, 37A30 
Moody, Robert V. Uniform Distribution in Model Sets. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 123-130. doi: 10.4153/CMB-2002-015-3
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