Koltchinskii an Gine study how discrete Laplacians constructed for randomly sampled points on a manifold approximate the true Laplacian: [Link](https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/High-Dimensional-Probability/chapter/Empirical-graph-Laplacian-approximation-of-LaplaceBeltrami-operators--Large-sample/10.1214/074921706000000888)