Statistical properties of interacting particles: universality and multiplicative chaos.

Seminar of Mathematics
Abstract:
Random matrix theory is a field of mathematics and physics, which aims at giving a statistical description of the spectral properties of large complex systems. The subject has a wide range of applications ranging from statistical physics, machine learning, number theory, etc.  The underpinning principle is that the (statistical) behavior of many complex systems should be universal and described by the laws of random matrix theory. I will report on some tremendous progress in understanding the behavior of large random matrices and other interacting particle systems which occurred in the past decade. I will also put these results in perspective with my own contribution to the study of characteristic polynomials of random matrices and the theory of multiplicative chaos.