Gap asymptotics of the directions in an Ammann-Beenker-like quasicrystal

2021/06/14 by Gustav Hammarhjelm, Hammarhjelm, Gustav
Materials Science · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Point processes and geometric inequalities #Probability (math.PR) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2106.07422

openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the limiting gap distribution of the directions to visible points in planar quasicrystals of cut-and-project type exists as a continuous function F(s). In this article we study the asymptotic behaviour of said limiting gap distribution in the particular case of an Ammann--Beenker-like quasicrystal P; more precisely we show that in this case F(s)=C_Ps^-2+O(s^-17/8) as s→ ∞ with an explicit constant C_P>0.

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