  We re-examine the nonperturbative curvature properties of two-dimensional
Euclidean quantum gravity, obtained as the scaling limit of a path integral
over dynamical triangulations of a two-sphere, which lies in the same
universality class as Liouville quantum gravity. The diffeomorphism-invariant
observable that allows us to compare the averaged curvature of highly
quantum-fluctuating geometries with that of classical spaces is the so-called
curvature profile. A Monte Carlo analysis on three geometric ensembles, which
are physically equivalent but differ by the inclusion of local degeneracies,
leads to new insights on the influence of finite-size effects. After
eliminating them, we find strong evidence that the curvature profile of 2D
Euclidean quantum gravity is best matched by that of a classical round
four-sphere, rather than the five-sphere found in previous work. Our analysis
suggests the existence of a well-defined quantum Ricci curvature in the scaling
limit.
