Concentration inequalities for the spectral measure of random matrices

Concentration Inequalities for the Spectral Measure of Random Matrices

where Y ∈ Rp×n is a rectangular p×n matrix with random centered entries, and both n and p ≤ n tend to infinity: typically p = p(n), and p(n)/n tends to some limit. M can be seen as the empirical covariance matrix of a random vector of dimension p sampled n times, each sample being a column of Y . It is common in applications to have a number of variables with a comparable order of magnitude wit...

Concentration of the Spectral Measure for Large Matrices

Concentration of the Spectral Measure for Large Random Matrices with Stable Entries

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value. AMS 2000 Subject Classification: 60E07, 60F10, 15A42, 15A52

Moderate Deviations for the Spectral Measure of Certain Random Matrices

– We derive a moderate deviations principle for matrices of the form XN = DN + WN where WN are Wigner matrices and DN is a sequence of deterministic matrices whose spectral measures converge in a strong sense to a limit μD . Our techniques are based on a dynamical approach introduced by Cabanal-Duvillard and Guionnet.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 60F99; 15A52

Estimation of Spectral Measure of Stable Random Vectors

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