Random walks on graphs and groups

Abstract:

We will introduce random walks, starting with random walks on the line and the plane. The study of these goes back to Polya, and they can be used as elementary models for both the stock market and the motion of particles. We will review some basic properties of these random walks, and discuss how they generalize to random walks on other spaces, in particular, those arising from the study of surfaces. We will also explain how random walks can be used to investigate ``generic" properties of these spaces.