Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities

We derive the joint distribution of the moments $\mathrm{T}\mathrm{r}{Q}^{\kappa }$ ($\kappa \ge 0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be asymptotically Gaussian, and we compute explicitly averages and covariances. The results are in a compact form and have been verified numerically. The general methodology of proof and computations has a wide range of applications.