Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

ASYMPTOTICS OF THE INERTIA MOMENTS AND THE VARIANCE CONJECTURE IN SCHATTEN BALLS

Abstract : We study the limit, as the dimension goes to infinity, of the moments of the Hilbert-Schmidt norm of a uniformly distributed matrix in the p-Schatten ball, with entries in the real, complex or quaternionic field. We also consider the restriction to the space of self-adjoint matrices. We build on the connection with spectral asymptotics of β-ensembles to adapt some fluctuation results due to Bekerman, Leblé and Serfaty [8]. When p > 3, this allows us to obtain the next asymptotic order for ratios of q-inertia moments of p-Schatten balls of self-adjoint matrices, and to establish a strong version of the variance conjecture for these families of convex bodies.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03428760
Contributor : Olivier Guédon Connect in order to contact the contributor
Submitted on : Monday, November 15, 2021 - 11:52:12 AM
Last modification on : Tuesday, November 16, 2021 - 3:56:26 AM

Files

2021-07-21-DFGZ.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03428760, version 1
  • ARXIV : 2111.07803

Collections

Citation

B Dadoun, M Fradelizi, Olivier Guédon, P.-A Zitt. ASYMPTOTICS OF THE INERTIA MOMENTS AND THE VARIANCE CONJECTURE IN SCHATTEN BALLS. 2021. ⟨hal-03428760⟩

Share

Metrics

Record views

19

Files downloads

15