Mixing of Random Substitutions

• Main Author: Tadeo, Gwendolyn
• Format: text
• Published: Archīum Ateneo 2019
• Subjects: topological mixing, random substitution, Fibonacci substitution, Pisot sub- stitution
• Online Access: https://archium.ateneo.edu/theses-dissertations/449
• Institution: Ateneo De Manila University

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.