Fluctuations and Large Deviations for Extreme Eigenvalues of Deformed Random Matrices
This is joint work with F.~Benaych Georges and Alice Guionnet.
We consider a model of matrices with well-known spectrum (deterministic with converging spectral measure, Wigner, Wishart etc.) and add a random perturbation with finite rank and delocalized eigenvectors. We get so called spiked or deformed models which lately received quite a lot of attention. We investigate the asymptotic behavior of their extreme eigenvalues, in particular their fluctuations and large deviations properties.