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An observation about submatrices

   
@article{ECP1504,
	author = {Sourav Chatterjee and Michel Ledoux},
	title = {An observation about submatrices},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {Random matrix, concentration of measure, empirical distribution, eigenvalue},
	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.},
	pages = {no. 48, 495-500},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1504},    
        url = {http://ecp.ejpecp.org/article/view/1504}}