On the principal components of sample covariance matrices

Following the pioneering work of [17] and [4,5] have shown universality of local eigenvalue statistics in the bulk of the spectrum for complex sample covariance matrices when

LPMA, UPMC Université Paris 6, Case courier 188, 4, Place Jussieu, 75252 Paris Cedex 05, France and CMAP, École Polytechnique, route de Saclay, 91128 Palaiseau Cedex, France. In

In particu- lar, if the multiple integrals are of the same order and this order is at most 4, we prove that two random variables in the same Wiener chaos either admit a joint

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

Second, the proof of the isotropic law in the case of sample covariance matrices is conceptually slightly clearer due to a natural splitting of summation indices into two

In [11], Capitaine, Donati-Martin, and F´ eral identified the law of the outliers of deformed Wigner matrices subject to the following conditions: (i) D is independent of N but may

Focusing more specifically on the eigenvectors corresponding to the largest and smallest non-zero eigen- values, Section 3 provides inequalities for the inner products c t v i using

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