Advanced Discrete Probability (Heydenreich)

We discuss a number of special topics in the theory of discrete random structures. The lecture covers both classical as well as very recent developments. The course is structures into five themes:

1. Markov chains on finite graphs, mixing time and cutoff phenomena
2. Random walk and electrical networks
3. Self-avoiding walk
4. Percolation
5. Erdös-Renyi random graphs

There is no written syllabus, but I give references to all topics discussed during the lecture.
The aim of the course is to make students acquainted with current research topics in this area. Ideal starting point for a master thesis in this area.