Automorphism groups of random substitution subshifts
Abstract
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.
Cite
@article{arxiv.2203.13545,
title = {Automorphism groups of random substitution subshifts},
author = {Robbert Fokkink and Dan Rust and Ville Salo},
journal= {arXiv preprint arXiv:2203.13545},
year = {2023}
}