## Electronic Journal of Probability

### Estimating the covariance of random matrices

Pierre Youssef

#### Abstract

We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for  positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we discuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 107, 26 pp.

Dates
Accepted: 19 December 2013
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465064332

Digital Object Identifier
doi:10.1214/EJP.v18-2579

Mathematical Reviews number (MathSciNet)
MR3151727

Zentralblatt MATH identifier
1287.60014

Rights

#### Citation

Youssef, Pierre. Estimating the covariance of random matrices. Electron. J. Probab. 18 (2013), paper no. 107, 26 pp. doi:10.1214/EJP.v18-2579. https://projecteuclid.org/euclid.ejp/1465064332

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