AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome… Expand

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue for some non-necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also… Expand

We consider sample covariance matrices $${S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}}$$ where XN is a N × p real or complex matrix with i.i.d. entries with finite 12th moment and ΣN is a N… Expand

We compute the limiting eigenvalue statistics at the edge of the spectrum of large Hermitian random matrices perturbed by the addition of small rank deterministic matrices. We consider random… Expand

It has been conjectured that both the distribution of the distance between nearest neighbor eigen values in the bulk and that of the smallest eigenvalues become, in the limit N → ∞, $${p \over N}$$ → 1, the same as that identified for a complex Gaussian distribution μ.Expand

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk… Expand

This paper extends the well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples to two cases, when the ratio approaches an arbitrary finite value and the ratio becomes infinite or arbitrarily small.Expand

On etudie la loi des plus grandes valeurs propres de matrices aleatoires symetriques reelles et de covariance empirique quand les coefficients des matrices sont a queue lourde. On etend le resultat… Expand

A generalization of the extended Airy kernel with two sets of real parameters is introduced that arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices.Expand