Ergodic frequency measures for random substitutions. (English) Zbl 1461.37018
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.
MSC:
| 37B10 | Symbolic dynamics |
| 37H12 | Random iteration |
| 37A25 | Ergodicity, mixing, rates of mixing |
| 52C23 | Quasicrystals and aperiodic tilings in discrete geometry |
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