  We show recent results of the application of spectral analysis in the setting
of the Monte Carlo approach to Quantum Gravity known as Causal Dynamical
Triangulations (CDT), discussing the behavior of the lowest lying eigenvalues
of the Laplace-Beltrami operator computed on spatial slices. This kind of
analysis provides information about running scales of the theory and about the
critical behaviour around a possible second order transition in the CDT phase
diagram, discussing the implications for the continuum limit.
