Mixing of Random Substitutions

Date of Award


Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

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.

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