Estimating the covariance of random matrices

Pierre Youssef (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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 in- terpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we dis- cuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices.

Domaines: Analyse fonctionnelle [math.FA]

Pierre Youssef. Estimating the covariance of random matrices. 2013. ⟨hal-00811808⟩