  In recent years several approaches to quantum gravity have found evidence for
a scale dependent spectral dimension of space-time varying from four at large
scales to two at small scales of order of the Planck length. The first evidence
came from numerical results on four-dimensional causal dynamical triangulations
(CDT) [Ambjorn et al., Phys. Rev. Lett. 95 (2005) 171]. Since then little
progress has been made in analytically understanding the numerical results
coming from the CDT approach and showing that they remain valid when taking the
continuum limit. Here we argue that the spectral dimension can be determined
from a model with fewer degrees of freedom obtained from the CDTs by "radial
reduction". In the resulting "toy" model we can take the continuum limit
analytically and obtain a scale dependent spectral dimension varying from four
to two with scale and having functional behaviour exactly of the form which was
conjectured on the basis of the numerical results.

High Energy Physics - Theory;General Relativity and Quantum Cosmology