Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices

The paper is concerned with deformed Wigner random matrices. These matrices are closely related to Deep Neural Networks (DNNs): weight matrices of trained DNNs could be represented in the form $R+S$, where $R$ is random and $S$ is highly correlated. The spectrum of such matrices plays a key role in rigorous underpinning of the novel pruning technique based on Random Matrix Theory. In practice, the spectrum of the matrix $S$ can be rather complicated. In this paper, we develop an asymptotic analysis for the case of full rank $S$ with increasing number of outlier eigenvalues.