Stationary C*-Dynamical Systems

We introduce the notion of stationary actions in the context of C-algebras, and prove a new characterization of C-simplicity in terms of unique stationarity. This ergodic theoretical characterization provides an intrinsic understanding for the relation between C-simplicity and the unique trace property, and provides a framework in which C-simplicity and random walks interact. Joint work with Mehrdad Kalantar.