Logic Seminar

The Poisson boundary of a random walk is a measure of the space of asymptotic non-trivial events that can occur for a random walk on a group. In this talk I will given an introduction to the notion of a Poisson boundary for a random walk on a countable group due to Furstenberg. I will define the Poisson boundary, explain the relationship between the Poisson boundary and harmonic functions, and explain the relationship between the Poisson boundary and amenability (due to Kaimanovich and Vershik) and the relationship between the Poisson boundary and the ICC property of groups. This is joint work with Yair Hartman, Omer Tamuz, and Pooya Vahidi Ferdowsi. No prior knowledge of random walks on groups will be assumed.