# Advanced Topics in Probability Theory, WS 2020/21

Time | Wednesday 10-12 and Friday, 8-10 |

Room | The lecture will be held digitally via Zoom. Links will be published on eCampus. You need to register here for the course. |

## Content

The **first part **of the lecture will be devoted on **random matrices**. In particular, we will study the eigenvalues in the Gaussian Unitary Ensemble of random matrices, whose eigenvalues serves as an example of determinantal point processes. We will then discuss this class of point process in a more general framework and develop some mathematical structure related to it.

The **second part **of the lecture deals with an **interacting particle system, the exclusion process**. We will discuss its construction and properties like stationary measures. For the totally asymmetric case, we will see how one can related it to the mathematical structure of the GUE matrices.

Finally, we will also discuss the large matrix size / large time limit, where *universal limit laws *and *processes *arises, which are different from the well-known Gaussian and Brownian motion.

**For more information, please contact me via email.**