Tomas Berggren: Central Limit Theorems for the Circular Unitary Ensemble and a transition to the Poisson Point Process

The Circular Unitary Ensemble (CUE) is a classical model within Random Matrix Theory. I will discuss the fluctuation of the model by means of Linear statistics and present Central Limit Theorems (CLTs). We will see that these limit theorems does not behave as the classical CLTs for the Poisson Point process. A transition, done by thinning, between these two types of CLTs will be investigated.