2022/03/25 by Robbert Fokkink, Fokkink, Robbert, D. M. Rust +3 · 1 citation
Computer Science · Materials Science · #37A50 #37B10 #37B40 #52C23 #Authorship Attribution and Profiling #Dynamical Systems (math.DS) #FOS: Mathematics #Quasicrystal Structures and Properties #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2203.13545
openalex publication_date 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.