Uniformly expanding random walks on manifolds

In this paper we construct uniformly expanding random walks on smooth manifolds. Potrie showed that given any open set U of ${\text{Diff}{\,}}_{\text{vol}}^\infty(\mathbb{T}^2)$, there exists an uniformly expanding random walk µ 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. Adapting to higher dimensions, we work with a new definition of uniform expansion that measures volume growth in subspaces rather than norm growth of single vectors.