Ergodic frequency measures for random substitutions
Volume 255 / 2020
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.
