  Numerical computations have suggested that in causal dynamical triangulation
models of quantum gravity the effective dimension of spacetime in the UV is
lower than in the IR. In this paper we develop a simple model based on previous
work on random combs, which share some of the properties of CDT, in which this
effect can be shown to occur analytically. We construct a definition for short
and long distance spectral dimensions and show that the random comb models
exhibit scale dependent spectral dimension defined in this way. We also observe
that a hierarchy of apparent spectral dimensions may be obtained in the
cross-over region between UV and IR regimes for suitable choices of the
continuum variables. Our main result is valid for a wide class of tooth length
distributions thereby extending previous work on random combs by Durhuus et al.
