Given tuples of properly normalized independent $N\times N$ G.U.E. matrices $(X_N^{(1)},\dots,X_N^{(r_1)})$ and $(Y_N^{(1)},\dots,Y_N^{(r_2)})$, we proved that the tuple $(X_N^{(1)}\otimes I_N,\dots,X_N^{(r_1)}\otimes I_N,I_N\otimes Y_N^{(1)},\dots,I_N\otimes Y_N^{(r_2)})$ of $N^2\times N^2$ random matrices converges strongly as $N$ tends to infinity. We will present the key steps and ideas of the proof. Note that it was shown by B. Hayes that this result implies that the Peterson-Thom conjecture is true.\ This is a joint work with Serban Belinschi.\ https://arxiv.org/abs/2205.07695v1.

Bio: Mireille Capitaine is a french mathematician. She has been a CNRS researcher since 1998 at the University Paul Sabatier, Toulouse. Her PHD under the guidance of Michel Ledoux was in the field of stochastic calculus. Since 2000, her research is in free probability theory and random matrices.