Estimating the covariance of random matrices
Résumé
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]
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estimating_the_covariance_of_random_matrices.pdf (364.4 Ko)
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