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arXiv · 2111.07803

Asymptotics of the Inertia Moments and the Variance Conjecture in Schatten Balls

Benjamin Dadoun·Matthieu Fradelizi·Olivier Guédon·Pierre-André Zitt
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Abstract

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.

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Benjamin Dadoun, Matthieu Fradelizi, Olivier Guédon, Pierre-André Zitt. 2021-11-15. Asymptotics of the Inertia Moments and the Variance Conjecture in Schatten Balls. https://arxiv.org/abs/2111.07803

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