Asymptotics of the inertia moments and the variance conjecture in Schatten balls

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...

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Bibliographic Details
Published inJournal of functional analysis Vol. 284; no. 2; p. 109741
Main Authors Dadoun, B., Fradelizi, M., Guédon, O., Zitt, P.-A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2023
Elsevier
Subjects
Asymptotic convex geometry
Functional Analysis
Inertia moments
Mathematics
Probability
Schatten balls
Variance conjecture
46B07
82B05
Inertia moments
Schatten balls
52A23
60B20
Variance conjecture
Asymptotic convex geometry
46B09
inertia moments
2021. 2020 Mathematics Subject Classification. 52A23
variance conjecture
82B05 Asymptotic convex geometry
November 15
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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2022.109741