- Enseignant-e: Johannes Alt
We continue the spectral analysis of random matrices from the course Random matrices and universality I in the last semester. The main goal of the lecture is understanding several instances of the universality phenomenon in random matrix theory. This is, that many microscopic statistics of a random matrix, i.e. statistics on the scale of the typical eigenvalue fluctuations, do not depend on fine details of the random matrix ensemble but solely its basic symmetry type. The basic tools will be Green function comparison theorems and a detailed analysis of Dyson Brownian motion, a stochastic dynamics on the eigenvalues of a matrix.