Random walks on groups and boundary theory 1000-1M26BL
1. A reminder on Markov chains and martingales.
2. Basic properties of random walks, such as speed and entropy.
3. Harmonic functions and the Poisson boundary.
4. Choquet-Deny theorem about absence of nontrivial harmonic funcitons on abelian groups.
5. Kaimanovich-Vershik theorem about existence of a trivial Poisson boundary for amenable groups.
If there is enough time:
6. Choquet-Deny theorem for nilpotent groups.
7. The Furstenberg boundary.
8. Applications of the boundary theory to the structure of group C*-algebras.
Course coordinators
Requirements
Assessment criteria
The final grade will depend on the participation and engagement in the classes and the final exam.
Bibliography
1. A. Yadin "Harmonic functions and random walks on groups"
2. V. Kaimanovich, A. Vershik "Random walks on discrete groups: boundary and entropy"
3. M. Kalantar, M. Kennedy "Boundaries of reduced C*-algebras of discrete groups"
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: