In addition to the paper arXiv:1301.2222 by Burago et al we can look in the following questions:

- work by S. Smirnov on discrete Cauchy-Riemann equations:
**Discrete Complex Analysis and Probability,****Discrete complex analysis and probability**(ICM 2010) and Discrete Complex Analysis - work of Giné and Koltchinskii:
**Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results** - using random walks and stochastic analysis to approximate the Laplacians on groups, such as the hypoelliptic Laplacian on the Heisenberg group, following Gordina and Laetsch
**Sub-Laplacians on Sub-Riemannian Manifolds**