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On the lower bound of the spectral norm of symmetric random matrices with independent entries


 
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1. Title Title of document On the lower bound of the spectral norm of symmetric random matrices with independent entries
 
2. Creator Author's name, affiliation, country Sandrine Peche; Institut Fourier, Grenoble, France
 
2. Creator Author's name, affiliation, country Alexander Soshnikov; University of California at Davis, USA
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Wigner random matrices, spectral norm
 
3. Subject Subject classification 15A52, 60C05.
 
4. Description Abstract We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \sigma - o( N^{-6/11+\varepsilon}), $ where $\sigma^2 $ is the variance of the matrix entries and $\varepsilon $ is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any $\varepsilon >0, \ $ one has $ \|A_N\| =2 \sigma + o( N^{-6/11+\varepsilon}) $ with probability going to $ 1 $ as $N \to \infty$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2008-06-01
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1376
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1376
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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