Topological Mixing of Random n-bonacci Substitutions

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Conference Proceeding

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We consider shift spaces generated by maps that send a letter from a finite alphabet to a finite collection of words over the same alphabet called random substitutions. In particular, we study the topological dynamics of the shift spaces associated with the family of random n-bonacci substitutions, which is a generalization of the random Fibonacci substitution. We establish that the random n-bonacci shift spaces are not topologically mixing by showing that the substitution admits recognisable words at every level through a specialized construction.