We will give the material for the course Advanced discrete probability on this webpage. In particular, a full set of lecture notes and exercise (with solutions) will be provided thoughout the course (together with suitable references).
The lectures takes place on Tuesday from 14:15 to 15:45 and Wednesday from 12:15 to 13:45 (rooms tba).
The course will cover the following topics:
An introduction to Markov processes, with a focus on invariant measures of interacting particle systems.
An overview on results for the stationary distribution of exclusion processes
An introduction to mixing times for Markov chains
Mixing times for exclusion processes using last passage percolation
As main reference, we refer to the book Markov chains and mixing times by Levin/Peres, in particular Chapters 1-5 for a basic introduction as well as 23 for recent developments on exclusion processes .
There will be an oral exam at the end of the course.