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

Random Matrix Theory (RMT) is a classical theory that has been developing for more than 70 years. Initially, RMT arose from problems in nuclear physics and found its applications in mathematics, physics, finance, and many other disciplines. Recently, new problems have been arising from the area of Machine Learning. Indeed, often the weight matrices of Deep Neural Networks (DNNs) are initialized randomly. Moreover, modern DNNs have large weight matrices, which is why their spectral properties can be described by asymptotic behavior of N N random matrices as N goes to infinity.