Lecturer: Prof. Dr. Sebastian Andres
Place and time: Tuesdays 13:15 - 14:45 in UP2.314
Prerequisites: Mathematical knowledge in basic measure theory and advanced probability theory is required. Knowledge of discrete Markov chains or analysis of partial differential equations is helpful but not essential.
Content: In this course we study the interactions between geometric properties of graphs, and the behaviour of random walks, transition densities, and harmonic functions. Specific topics include
- Graphs and weighted graphs (Examples and Geometric Properties)
- Random walks
- Transition densities and the Laplacian
- Dirichlet or energy form
- Green functions, Harmonic functions, Harnack inequalities
- Isoperimetric inequality, Nash inequality, Poincare inequality
- Heat Kernel estimates
Seminar: In addition to the lectures we will run a student seminar with closely related topics, details will be discussed in the first session.
Literature: