Explore large deviations for sub-Riemannian random walks on homogeneous Carnot groups in this one-hour lecture from the Hausdorff Center for Mathematics. Delve into the proof of a Large Deviations Principle (LDP) and discover how to identify a natural rate function for these random walks as an energy functional. Compare standard Brownian motion to Brownian motion in the Heisenberg group, and examine the hypoelliptic Brownian motions corresponding to these sub-Riemannian random walks. The talk, presented by Mascha Gordina, is based on joint work with Tai Melcher, Jing Wang, and others, offering insights into advanced mathematical concepts at the intersection of probability theory and differential geometry.