Large deviations of the extreme eigenvalues of random deformations of matrices


Consider a real diagonal deterministic matrix Xn of size n with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, with delocalized eigenvectors. We show that the joint law of the extreme eigenvalues of the perturbed model satisfies a large deviation principle in the scale… (More)