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Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices


 
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1. Title Title of document Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices
 
2. Creator Author's name, affiliation, country Arup Bose; Indian Statistical Institute
 
2. Creator Author's name, affiliation, country Arnab Sen; University of California, Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large dimensional random matrix, eigenvalues, Wigner matrix, Toeplitz matrix, Hankel matrix, spectral norm.
 
3. Subject Subject classification Primary 60F99; Secondary 60F05, 60F15
 
4. Description Abstract Suppose $s_n$ is the spectral norm of either the Toeplitz or the Hankel matrix whose entries come from an i.i.d. sequence of random variables with positive mean $\mu$ and finite fourth moment. We show that $n^{-1/2}(s_n-n\mu)$ converges to the normal distribution in either case. This behaviour is in contrast to the known result for the Wigner matrices where $s_n-n\mu$ is itself asymptotically normal.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2007-02-13
 
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/1243
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1243
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
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