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

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.

Citation

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Sourav Chatterjee. Michel Ledoux. "An observation about submatrices." Electron. Commun. Probab. 14 495 - 500, 2009. https://doi.org/10.1214/ECP.v14-1504

Information

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

Subjects:
Primary: 60E15
Secondary: 15A52

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