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Explore a 28-minute lecture on uniformly expanding random walks on manifolds, presented by Rose Elliott Smith from the University of Chicago as part of the Simons Semester on Dynamics. Delve into the dynamical property of uniform expansion, which indicates a system's average expansion everywhere. Learn about the strong Ratner-like orbit and measure classification theorems for this class of random walks, as demonstrated in the in-progress work of Brown, Eskin, Filip, and Rodriguez Hertz. Investigate key questions surrounding the prevalence of uniformly expanding random walks and the contexts in which they can exist. Gain insights into this fascinating area of mathematical study and its implications for understanding dynamical systems.
