Abstract
The third lecture was entirely devoted to an introduction to the theory of Gaussian Unitary Ensemble (GUE) random matrices. First, classical results on the density and correlations of eigenvalues of random matrices were recalled, as well as the many fields of physics or mathematics where they are studied (nuclear physics, quantum chaos, Riemann zeta function...) The lecture continued by showing how these results follow from a representation of the eigenvalue distribution in terms of the energies of a system of free fermions, which can be calculated by a semi-classical treatment.
