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

2021/11/15 by Dadoun, Benjamin, Fradelizi, Matthieu, Guédon, Olivier +1 · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.07803

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.

Cited by

• Next-order asymptotics for the volume of Schatten balls
• Thin-shell bounds via parallel coupling

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