Asymptotic estimates of large gaps between directions in certain planar quasicrystals

2024/09/29 by Gustav Hammarhjelm, Hammarhjelm, Gustav, Andreas Strömbergsson +3 · 1 citation
Materials Science · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Probability (math.PR) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2409.19514

openalex publication_date 2024/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For quasicrystals of cut-and-project type in ℝ^d, it was proved by Marklof and Strömbergsson that the limit local statistical properties of the directions to the points in the set are described by certain SL_d(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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