  We investigate topological mixing of compatible random substitutions. For
primitive random substitutions on two letters whose second eigenvalue is
greater than one in modulus, we identify a simple, computable criterion which
is equivalent to topological mixing of the associated subshift. This
generalises previous results on deterministic substitutions. In the case of
recognisable, irreducible Pisot random substitutions, we show that the
associated subshift is not topologically mixing. Without recognisability, we
rely on more specialised methods for excluding mixing and we apply these
methods to show that the random Fibonacci substitution subshift is not
topologically mixing.
