Mathematics

Random matrix theory was pioneered in the 1920s by the statistician John Wishart to tackle empirical covariance matrices and in the 1950s by Eugene Wigner to study heavy nuclei. It has since expanded to multiple branches of mathematics from number theory to statistical physics. In this talk we will consider recent advances regarding the large deviations of spectra of random matrices whose dimension goes to infinity. In other words we want to quantify how fast the probability that those spectra (and in particular the largest eigenvalue) being close to a value different from their limit vanishes. Linked to this question, we also consider the asymptotics of spherical integrals, which in addition to being rich mathematical objects, have played an instrumental role in the previously mentioned advances.