2023/10/31 by Roca, Daniel
Computer Science · Materials Science · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2310.20517
openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study hyperuniformity of self-similar point processes arising from substitution rules in two dimensions. In particular, we derive a sufficient condition for hyperuniformity of these point processes only in terms of the associated substitution matrix. This condition applies to a wide class of examples for which hyperuniformity had not yet been established, including most well-known examples of planar self-similar tilings. In particular, we show that the Godrèche-Lançon-Billard substitution rule gives rise to hyperuniform point processes with singular continuous diffraction. Furthermore, we prove that hyperuniformity is not an MLD invariant, contradicting standing conjectures.