Maurice Duits: Fluctuations of linear statistics in random matrix theory

Linear statistics provide an important tool in the analysis of various point processes in random matrix theory. The fluctuations of such linear statistics for large systems can often be described in terms of Central Limit Theorems. These Central Limit Theorems have a rather different character compared to the standard Central Limit Theorem for independent random variables and can be viewed as a manifestation of the repulsive interaction between the points in the system, which is characteristic for random matrix models. This talk will be a self-contained introduction to the topic and will be based on a discussion of several important examples.