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An observation about submatrices


 
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1. Title Title of document An observation about submatrices
 
2. Creator Author's name, affiliation, country Sourav Chatterjee; University of California at Berkeley
 
2. Creator Author's name, affiliation, country Michel Ledoux; Institut de Mathematiques, Universite de Toulouse
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrix, concentration of measure, empirical distribution, eigenvalue
 
3. Subject Subject classification 60E15, 15A52
 
4. Description Abstract Let $M$ be an arbitrary Hermitian matrix of order $n$, and $k$ be a positive integer less than $n$. We show that if $k$ is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of $M$ of order $k$. The proof uses results about random walks on symmetric groups and concentration of measure. In a similar way, we also show that almost all $k \times n$ submatrices of $M$ have almost the same distribution of singular values.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF grant DMS-0707054, Sloan Research Fellowship, ANR Grandes Matrices Aleatoires
 
7. Date (YYYY-MM-DD) 2009-11-05
 
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/1504
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1504
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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