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We investigate topological mixing of compatible random substitutions. Forprimitive random substitutions on two letters whose second eigenvalue isgreater than one in modulus, we identify a simple, computable criterion whichis equivalent to topological mixing of the associated subshift. Thisgeneralises previous results on deterministic substitutions. In the case ofrecognisable, irreducible Pisot random substitutions, we show that theassociated subshift is not topologically mixing. Without recognisability, werely on more specialised methods for excluding mixing and we apply thesemethods to show that the random Fibonacci substitution subshift is nottopologically mixing.

Topological Mixing of Random Substitutions