From Berry-Esseen to super-exponential

Klara Courteaut, Kurt Johansson, Gaultier Lambert

For any integer $m<n$, where $m$ can depend on $n$, we study the rate of convergence of $\frac{1}{\sqrt{m}}\mathrm{Tr}{\mathbf{U}}^m$ to its limiting Gaussian as $n\to \infty$ for or…