Deformed ensembles of random matrices

In this article, we review recent results in the study of asymptotic spectral properties of some perturbation of large random matrices. Deformed models have arisen in random matrix theory in Baik, J.; Ben Arous, G.; Peche S. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 (2005), no. 5, 1643-1697. In this review, we consider additive or multiplicative deformations of standard Wigner or sample covariance matrices. We consider the phenomenon of separation of extreme eigenvalues and the question of universality of their asymptotic distribution for random matrices with a non necessarily Gaussian distribution.