Open Access
2009 An observation about submatrices
Sourav Chatterjee, Michel Ledoux
Author Affiliations +
Electron. Commun. Probab. 14: 495-500 (2009). DOI: 10.1214/ECP.v14-1504


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.


Download Citation

Sourav Chatterjee. Michel Ledoux. "An observation about submatrices." Electron. Commun. Probab. 14 495 - 500, 2009.


Accepted: 5 November 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60041
MathSciNet: MR2559099
Digital Object Identifier: 10.1214/ECP.v14-1504

Primary: 60E15
Secondary: 15A52

Keywords: concentration of measure , eigenvalue , Empirical distribution , Random matrix

Back to Top