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

Benhamou, Eric; Atif, Jamal; Laraki, Rida (2019-01), A short note on the operator norm upper bound for sub-Gaussian tailed random matrices. https://basepub.dauphine.fr/handle/123456789/18906

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1812.09618v2.pdf (165.3Kb)
Type
Document de travail / Working paper
Date
2019-01
Publisher
Preprint Lamsade
Series title
Preprint Lamsade
Published in
Paris
Pages
12
Metadata
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Author(s)
Benhamou, Eric
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Atif, Jamal
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Laraki, Rida cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
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.
Subjects / Keywords
sub-Gaussian tailed random matrices

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