I will talk about the work of Aizenman, Peled, Schenker, Shamis and Sodin, studying the regularizing effect of the gaussian random noise to the spectral structure of a Hermitian matrix. The authors obtain the estimates for the norm of the inverse of A + V (where A is a base matrix, V is a random gaussian noise) and for the average number of its eigenvalues inside an interval. We will mainly focus on the proof techniques: there is a nice collection of the probabilistic and Fourier-analytic methods employed in the proof. Speaker(s): Liza Rebrova (UM)