Curvature profiles for quantum gravity

Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative gravity, we advocate a new, global observable for curved metric spaces, profile. It is obtained integrating scale-dependent, quasilocal curvature, therefore also depends coarse-graining scale. To understand how distribution local, Gaussian reflected profile, compute it class regular, two-dimensional polygons with isolated conical singularities. We focus case tetrahedron, which have good computational control its geodesics, compare profile to that smooth sphere. The two are distinct, but qualitatively similar, confirms has averaging properties interesting from point view.