  Correlation functions are ubiquitous tools in quantum field theory from both
a fundamental and a practical point of view. However, up to now their use in
theories of quantum gravity beyond perturbative and asymptotically flat regimes
has been limited, due to difficulties associated with diffeomorphism invariance
and the dynamical nature of geometry. We present an analysis of a manifestly
diffeomorphism-invariant, nonperturbative two-point curvature correlator in
two-dimensional Lorentzian quantum gravity. It is based on the recently
introduced quantum Ricci curvature and uses a lattice regularization of the
full path integral in terms of causal dynamical triangulations. We discuss some
of the subtleties and ambiguities in defining connected correlators in theories
of dynamical geometry, and provide strong evidence from Monte Carlo simulations
that the connected two-point curvature correlator in 2D Lorentzian quantum
gravity vanishes. This work paves the way for an analogous investigation in
higher dimensions.
