Spectral properties of large random matrices with independent entries (Q2905542)

The authors consider large Wigner random matrices. In Section 2, they study the fluctuations of the \(k\)-th eigenvalue of a random matrix around the appropriate quantile of the Wigner semicircle law in the regime when \(k,n, n-k\to\infty\). They discuss some of the results by \textit{T. Tao} and \textit{V. Vu} [Acta Math. 206, No. 1, 127--204 (2011; Zbl 1217.15043)] for some ensembles of random matrices including Wigner real symmetric random matrices and the Wishart ensemble of sample covariance matrices. Section 3 is devoted to finite rank perturbations of Wigner random matrices. They extend the results by \textit{M. Capitaine, C. Donati-Martin} and \textit{D. Féral} [Ann. Probab. 37, No. 1, 1--47 (2009; Zbl 1163.15026)] by lifting the assumption of the symmetry of the marginal distribution. In Sections 4 and 5, the authors apply the resolvent technique to study recursive relations for local linear statistics in the bulk and at the edge of the spectrum of large random matrices.NEWLINENEWLINEFor the entire collection see [Zbl 1248.46002].