Abstract
It is well known that a positive proportion of all points in a d-dimensional lattice is visible from the origin, and that these visible lattice points have constant density in R-d. In the present paper, we prove an analogous result for a large class of quasicrystals, including the vertex set of a Penrose tiling. We furthermore establish that the statistical properties of the directions of visible points are described by certain SL(d, R)-invariant point processes. Our results imply in particular existence and continuity of the gap distribution for directions in certain 2D cut-and-project sets. This answers some of the questions raised by Baake et al. [1].
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