  This paper deals with (globally) random substitutions on a finite set of
prototiles. Using renormalization tools applied to objects from operator
algebras we establish upper and lower bounds on the rate of deviations of
ergodic averages for the uniquely ergodic $\mathbb{R}^d$ action on the tiling
spaces obtained from such tilings. We apply the results to obtain statements
about the convergence rates for integrated density of states for random
Schr\"odinger operators obtained from aperiodic tilings in the construction.
