Georgia Institute of Technology College of Sciences

A sub-Riemannian manifold M is a connected smooth manifold such that the only smooth curves in M which are admissible are those whose tangent vectors at any point are restricted to a particular subset of all possible tangent vectors.  Such spaces have several applications in physics and engineering, as well as in the study of hypo-elliptic operators.  We will  construct a random walk on M which converges to a process whose infinitesimal generator  is  one of the natural sub-elliptic  Laplacian  operators.  We will also describe these  Laplacians geometrically and discuss the difficulty of defining one which is canonical.   Examples will be provided.  This is a joint work with Tom Laetsch.