A new approach to strong convergence II. The classical ensembles

Understand

The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments.

• This method was applied to achieve a refined qualitative and quantitative understanding of strong convergence of random permutation matrices and of more general representations of the symmetric group.
• In this paper, we introduce new ideas that make it possible to achieve stronger quantitative results and that facilitate the application of the method to new models.
• When applied to the Gaussian GUE/GOE/GSE ensembles of dimension $N$, these methods achieve strong convergence for noncommutative polynomials with matrix coefficients of dimension $\exp(o(N))$.