  We present results on the behavior of the boundary-boundary correlation
function of scalar fields propagating on discrete two-dimensional random
triangulations representing manifolds with the topology of a disk. We use a
gravitational action that includes a curvature squared operator, which favors a
regular tessellation of hyperbolic space for large values of its coupling. We
probe the resultant geometry by analyzing the propagator of a massive scalar
field and show that the conformal behavior seen in the uniform hyperbolic space
survives as the coupling approaches zero. The analysis of the boundary
correlator suggests that holographic predictions survive, at least, weak
quantum gravity corrections. We then show how such an $R^2$ operator might be
induced as a result of integrating out massive lattice fermions and show
preliminary result for boundary correlation functions that include the effects
of this fermionic backreaction on the geometry.
