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A short note on the operator norm upper bound for sub-Gaussian tailed random matrices

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Date
2019-01
Publisher city
Paris
Publisher
Preprint Lamsade
Publishing date
2019
Collection title
Preprint Lamsade
Link to item file
https://arxiv.org/abs/1812.09618v2
Dewey
Analyse
Sujet
sub-Gaussian tailed random matrices
URI
https://basepub.dauphine.fr/handle/123456789/18906
Collections
  • LAMSADE : Publications
Metadata
Show full item record
Author
Benhamou, Eric
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Atif, Jamal
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Laraki, Rida
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Document de travail / Working paper
Item number of pages
12
Abstract (EN)
This paper investigates an upper bound of the operator norm for sub-Gaussian tailed random matrices. A lot of attention has been put on uniformly bounded sub-Gaussian tailed random matrices with independent coefficients. However, little has been done for sub-Gaussian tailed random matrices whose matrix coefficients variance are not equal or for matrix for which coefficients are not independent. This is precisely the subject of this paper. After proving that random matrices with uniform sub-Gaussian tailed independent coefficients satisfy the Tracy Widom bound, that is,their matrix operator norm remains bounded by O(√n) with overwhelming probability, we prove that a less stringent condition is that the matrix rows are independent and uniformly sub-Gaussian. This does not impose in particular that all matrix coefficients are independent, but only their rows, which is a weaker condition.

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