Measure theoretic entropy of random substitutions

Abstract: Random substitutions and their associated subshifts provide a model for structures that exhibit both long range order and positive entropy. In this talk we discuss the entropy of a large class of ergodic measures, known as frequency measures, that arise naturally from random substitutions. We introduce a new measure of complexity, namely measure theoretic inflation word entropy, and discuss its relationship to measure theoretic entropy. We also show how this new measure of complexity can be used to provide a framework for the systematic study of the measure theoretic entropy of random substitution subshifts.

As an application of our results, we obtain closed form formulas for the entropy of a wide range of random substitution subshifts and show that in many cases there exists a frequency measure of maximal entropy. Further, for a class of random substitution subshifts, we show that this measure is the unique measure of maximal entropy.

This is joint work with P. Gohlke, R. Leek, D. Rust, and T. Samuel.

dynamical systems

Audience: researchers in the topic

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Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

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