Concentration of the Spectral Measure for Large Matrices

Concentration of the Spectral Measure for Large 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 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

Concentration of the Spectral Measure of Large Wishart Matrices with Dependent Entries

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

Spectral Measure of Large Random Hankel, Markov and Toeplitz Matrices

We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {Xk} of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables {Xij}j>i of zero mean and unit variance, scaling the eigenvalues by √ n we prove the almost sure, weak convergence of the spectr...