Multivariate normal approximation for traces of orthogonal and symplectic matrices

Klara Courteaut, Kurt Johansson

We show that the distance in total variation between $(\mathrm{Tr}U,\frac{1}{\sqrt{2}}\mathrm{Tr}{U}^2,\cdots ,\frac{1}{\sqrt{m}}\mathrm{Tr}{U}^m)$ and a real Gaussian vector,…