Mixing of Random Substitutions
Date of Award
Doctor of Philosophy in Mathematics
Eden Delight P. Miro, PhDDaniel Rust, PhD
This dissertation investigates mixing properties of compatible random substitutions on two letters. The characterization of the mixing properties of this class of substitu- tions relies on the second eigenvalue of the associated substitution matrix. We present necessary and sufficient conditions for non-Pisot compatible random substitutions de- fined on two letters to be topologically mixing. This generalizes previous results on deterministic substitutions. As an intermediate result, we provide a total classification of two-letter primitive periodic substitutions. Another notion of mixing called semi- mixing is introduced which is shown to be satisfied by compatible Pisot random sub- stitutions arising from variants of the Fibonacci substitution, whose mixing properties have not been fully established.
(2019). Mixing of Random Substitutions. Ateneo de Manila University.