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In this paper we survey the theory of random walks on buildings andassociated groups of Lie type and Kac-Moody groups. We begin with anintroduction to the theory of Coxeter systems and buildings, taking a largelycombinatorial perspective. We then survey the theory of random walks onbuildings, and show how this theory leads to limit theorems for random walks onthe associated groups.

Buildings, groups of Lie type, and random walks