Uniformly Expanding Random Walks on Manifolds

In this talk we will study a dynamical property called uniform expansion— this property tells us that a system is, on average, expanding everywhere. An in-prep work of Brown, Eskin, Filip, and Rodriguez Hertz proves strong Ratner-like orbit and measure classification theorems specific to this class of random walks. With motivation from this work, we ask and answer a few natural questions, building on the work of Potrie: how common are uniformly expanding random walks, and in what settings can they exist?