Ergodic frequency measures for random substitutions

We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of every finite legal word exist for almost every element of the random substitution subshift with respect to these measures. A...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Gohlke, Philipp, Spindeler, Timo
Format: Article
Language:English
Subjects:
Ergodic processes
Substitutes
Online Access:Get full text
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Summary:We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of every finite legal word exist for almost every element of the random substitution subshift with respect to these measures. As an application, we show that for a certain class of random substitutions the measures of maximal entropy are frequency measures.
ISSN:2331-8422