  The spectrum of the Laplace-Beltrami operator, computed on the spatial slices
of Causal Dynamical Triangulations, is a powerful probe of the geometrical
properties of the configurations sampled in the various phases of the lattice
theory. We study the behavior of the lowest eigenvalues of the spectrum and
show that this can provide information about the running of length scales as a
function of the bare parameters of the theory, hence about the critical
behavior around possible second order transition points in the CDT phase
diagram, where a continuum limit could be defined.
