Isotropic local laws for sample covariance and generalized Wigner matrices

Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law.. Our approach

The contribution to the expectation (12) of paths with no 1-edges has been evaluated in Proposition 2.2. This section is devoted to the estimation of the contribution from edge paths

We establish a large deviation principle for the empirical spec- tral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo’s result

Before studying the impact of the number of frames L n to estimate the noise and the noisy SCMs, the number of sensors M and the SCMs-ICC ρ on the performance of the MWF, this

Under a mild dependence condition that is easily verifiable in many situations, we derive that the limiting spectral distribution of the associated sample covariance matrix

The argument de- veloped in Section 2 in order to extend the GUE results to large families of Hermitian Wigner matrices can be reproduced to reach the desired bounds on the variances

The recent references [BFG + 15] and [FBD15] provide asymptotic results for maximum likelihood approaches, and require that the smallest eigenvalue of the covariance matrix of

Various techniques have been developed toward this goal: moment method for polynomial functions ϕ (see [2]), Stieltj`es transform for analytical functions ϕ (see [4]) and