Electronic Communications in Probability

An observation about submatrices

Sourav Chatterjee and Michel Ledoux

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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.

Article information

Source
Electron. Commun. Probab. Volume 14 (2009), paper no. 48, 495-500.

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

Permanent link to this document
http://projecteuclid.org/euclid.ecp/1465234757

Digital Object Identifier
doi:10.1214/ECP.v14-1504

Mathematical Reviews number (MathSciNet)
MR2559099

Zentralblatt MATH identifier
1189.60041

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 15A52

Keywords
Random matrix concentration of measure empirical distribution eigenvalue

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Chatterjee, Sourav; Ledoux, Michel. An observation about submatrices. Electron. Commun. Probab. 14 (2009), paper no. 48, 495--500. doi:10.1214/ECP.v14-1504. http://projecteuclid.org/euclid.ecp/1465234757.


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