Measure theoretic entropy of random substitutions
Andrew Mitchell (University of Birmingham)
Abstract: Random substitutions and their associated subshifts provide a model for structures that exhibit both long range order and positive topological 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. This new measure of complexity provides a framework for the systematic study of measure theoretic entropy for random substitution subshifts.
As an application of our results, we obtain closed form formulas for the entropy of frequency measures for 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 talk is based on joint work with P. Gohlke, D. Rust, and T. Samuel.
dynamical systemsnumber theory
Audience: researchers in the topic
( slides )
Series comments: Description: Online seminar on numeration systems and related topics
For questions or subscribing to the mailing list, contact the organisers at numeration@irif.fr
| Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
| *contact for this listing |