Random Walks on Groups

In October 2024, I gave a talk at Peer Mathematics Seminar, a weekly peer seminar held in Department of Mathematical Sciences, Seoul National University. I discussed the construction of random walks on groups and introduced important concepts that appear in this field: harmonic functions, the Poisson–Furstenberg boundary, and Avez asymptotic entropy.

Abstract

Random walks on groups were first introduced by Kesten in 1959. The study of these random walks has become a valuable method for exploring group structures, leading to many intriguing questions. In this talk, we will discuss the construction of random walks on groups and introduce some fundamental concepts, such as harmonic functions, the Poisson–Furstenberg boundary, and Avez asymptotic entropy.

Lecture Note

These are hand-written notes for my talk.