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Ergodic frequency measures for random substitutions

Volume 255 / 2020

Philipp Gohlke, Timo Spindeler Studia Mathematica 255 (2020), 265-301 MSC: Primary 37B10, 37A25; Secondary 37A50, 52C23. DOI: 10.4064/sm181026-14-8 Published online: 4 May 2020

Abstract

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.

Authors

  • Philipp GohlkeFakultät für Mathematik
    Universität Bielefeld
    Postfach 100131
    33501 Bielefeld, Germany
    e-mail
  • Timo SpindelerDepartment of Mathematical and Statistical Sciences
    632 CAB, University of Alberta
    Edmonton, AB, T6G 2G1, Canada
    e-mail

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