  We derive general properties of the scale-dependent effective spectral
dimensions of non-perturbative gauge boson propagators as they appear as
solutions from different methods in Yang-Mills theories. In the ultraviolet and
for short time scales the anomalous dimensions of the propagators lead to a
slight decrease of the spectral dimension as compared to the one of a free
propagator. Lowering the momentum scale, the spectral dimension decreases
further. The class of propagators which display a maximum at Euclidean momenta,
and thus violate positivity, always approaches a spectral dimension of one for
large times. We also show that the longest time intervals are not related to
the deep infrared but to the momentum scale defined by the position of the
maximum.
