Kevin Schnelli: Tracy-Widom distribution for a general class of random matrices

In the first part of this talk, I will give an introduction to the
universality phenomenon in random matrix theory. In the second part, I
will focus on the edge universality which assert that the largest
eigenvalues of a large class of random matrices follow the Tracy-Widom
laws. I will then discuss basic concepts and tools to derive the edge
universality, and I will present recent edge universality results for
sample covariance matrices and for adjacency matrices of Erdős-Rényi
graphs.