Random Walks in Groups

The course will follwo the book "Random Walks on Infinite Groups" by Steven P. Lalley.

Content

There will be three main parts in the course. First, we will introduce the notion of a random walk, and study its basic properties in the setting of groups. Second, we will introduce a tool called the Poisson boundary, a boundary associated to groups via random walks. Third, we will study random walks in the context of hyperbolic groups.

Prerequisites

The course assumes knowledge about geometric group theory, specifically Cayley graphs and hyperbolic groups. Students who did not attend last semester's "Introduction to geometric group theory course" but want to take this course regardless are recommended to read chapters 1-3 of the book "Office hours with a geometric group theorist". The course also requires foundational knowledge of probability theory (random variables, variance, mean and knowledge of martingales is helpful. The concepts needed for the course are also outlined in the appendix of the Book "Random Walks on Infinite Groups" by Steven P. Lalley.

Exam

There will be oral exams held on August 3rd, 5th and 6th. The register, make sure that you are properly signed up in Basis and send an email to Heike Backer (bacher@math...) with two preferred time slots in the form of morning/afternoon + date, she will then coordinate a specific timeslot with you. The deadline to register for the exams is July 23rd. There will be a second period of exams at the end of September, exact dates and registration deadline will be announced on a later date.