Asymptotics of the Inertia Moments and the Variance Conjecture in Schatten Balls
Benjamin Dadoun, Matthieu Fradelizi, Olivier Guédon, Pierre-André Zitt · arXiv (Cornell University) · 2021
We study the first and second orders of the asymptotic expansion, as the dimension goes to infinity, of the moments of the Hilbert-Schmidt norm of a uniformly distributed matrix in the p-Schatten unit ball. We consider the case of matrices with real, complex or quaternionic entries, self-adjoint or not. When p > 3, this asymptotic expansion allows us to establish a generalized version of the variance conjecture for the family of p-Schatten unit balls of self-adjoint matrices.