Uniformly Expanding Random Walks on Manifolds

In this paper we construct uniformly expanding random walks on smooth manifolds. In higher dimensions, our definition of uniform expansion measures the growth of subspaces rather than single vectors. Potrie showed that given any open set $U$ of ${\text{Diff}}_{vol}^{\mathrm{\infty }}({\mathbb{T}}^2)$, there exists an uniformly expanding random walk $\mu$ supported on a finite subset of $U$. In this paper we extend those results to closed manifolds of any dimension, building on the work of Potrie and Chung to build a robust class of examples.