Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example for this is that independent GUE random matrices converge to free semicircular operators, which generate the free group von Neumann algebra. The usual convergence in distribution has been strengthened in recent years to a strong convergence, also taking operator norms into account. All this is on the level of polynomials. In my talk I will recall this and then go over from polynomials to rational functions (in non-commuting variables). Unbounded operators will also play a role.