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Developments and Open Problems

IMS Distinguished Visitor Lecture Series An Introduction to Intertwining via Strong Stationary Duality Lecture 4: Developments and Open Problems Persi Diaconis Stanford University, USA Many of the examples where Dual chains can be usefully constructed are for random walk on groups where stationary distributions are uniform. Applications in statistics call for constructions with less symmetry. I will illustrate this using Nestoridi's construction of stationary times for random walks on the chambers of a hyperplane arrangement and through Igor Pak's many examples of non-uniform duals.