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arXiv · 2409.19514

Asymptotic estimates of large gaps between directions in certain planar quasicrystals

Gustav Hammarhjelm·Andreas Strömbergsson·Shucheng Yu
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Abstract

For quasicrystals of cut-and-project type in $\mathbb{R}^d$, it was proved by Marklof and Str\"ombergsson that the limit local statistical properties of the directions to the points in the set are described by certain $\operatorname{SL}_d(\mathbb{R})$-invariant point processes. In the present paper we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals.

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Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu. 2024-09-29. Asymptotic estimates of large gaps between directions in certain planar quasicrystals. https://arxiv.org/abs/2409.19514

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