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 | |
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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