Visibility and Directions in Quasicrystals
2015 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 15, 6588-6617 p.Article in journal (Refereed) Published
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. .
Place, publisher, year, edition, pages
2015. no 15, 6588-6617 p.
IdentifiersURN: urn:nbn:se:uu:diva-262010DOI: 10.1093/imrn/rnu140ISI: 000359716500021OAI: oai:DiVA.org:uu-262010DiVA: diva2:851784
FunderEU, FP7, Seventh Framework Programme, 291147