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On the expectation of the norm of random matrices with non-identically distributed entries


 
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1. Title Title of document On the expectation of the norm of random matrices with non-identically distributed entries
 
2. Creator Author's name, affiliation, country Carsten Schuett; Christian-Albrechts Universität; Germany
 
2. Creator Author's name, affiliation, country Stiene Riemer; Christian-Albrechts Universität; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Matrix; Largest Singular Value; Orlicz Norm
 
3. Subject Subject classification 46B09; 46B45; 60G50
 
4. Description Abstract

Let $X_{i,j}$, $i,j=1,...,n$, be independent, not necessarily identically distributed random variables with finite first moments. We show that the norm of the random matrix $(X_{i,j})_{i,j=1}^n$ is up to a logarithmic factor of the order of $\mathbb{E}\max\limits_{i=1,...,n}\left\Vert(X_{i,j})_{j=1}^n\right\Vert_2+\mathbb{E}\max\limits_{i=1,...,n}\left\Vert(X_{i,j})_{j=1}^n\right\Vert_2$. This extends (and improves in most cases) the previous results of Seginer and Latala.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-02-22
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2103
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2103
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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