Coarse Ricci curvature with applications to manifold learning problem

Consider a sample of $n$ points taken i.i.d from a submanifold of Euclidean space. This defines a metric measure space. We show that there is an explicit set of scales $t_{n}\rightarrow0$ such that a coarse Ricci curvature at scale $t_{n}$ on this metric measure space converges almost surely to the coarse Ricci curvature of the underlying manifold.