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

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03428760
Contributor : Pierre-André Zitt Connect in order to contact the contributor
Submitted on : Tuesday, February 15, 2022 - 11:33:44 AM
Last modification on : Wednesday, April 13, 2022 - 9:33:27 AM

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2022-02-04-DFGZ.pdf
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  • HAL Id : hal-03428760, version 2
  • ARXIV : 2111.07803

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Benjamin Dadoun, Matthieu Fradelizi, Olivier Guédon, Pierre-André Zitt. Asymptotics of the Inertia Moments and the Variance Conjecture in Schatten Balls. 2022. ⟨hal-03428760v2⟩

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