Gaultier Lambert (University of Zürich): Fluctuations of smooth eigenvalues statistics for random matrices

The eigenvalues of random matrices are basic examples of point processes with strong correlations and their scaling limits are very different from that of independent points. After a short presentation of the so-called circular unitary ensemble (CUE) and Gaussian unitary ensemble (GUE), I am planning to discuss proofs of the central limit theorem for smooth linear statistics for both models. The method is elementary and the talk aims at a general audience.