Large deviations principle for sub-Riemannian random walks

Abstract

We study large deviations for random walks on stratified (Carnot) Lie groups. For such groups, there is a natural collection of vectors which generates their Lie algebra, and we consider random walks with increments in only these directions. Under certain constraints on the distribution of the increments, we prove a large deviation principle for these random walks with a natural rate function adapted to the sub-Riemannian geometry of these spaces.

This version is greatly revised and expanded in scope to include the case of sub-Riemannian random walks with Gaussian samples in Carnot groups of any step. A new author, Dan Mikulincer, has been added. Comments are welcome