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.
Orthogonal and symplectic matrix models: universality and other properties
Orthogonal and symplectic matrix models with real analytic potentials and multi interval supports of the equilibrium measures will be discussed. For these models bulk universality of local eigenvalue statistics and bounds for the rate of convergence of linear eigenvalue statistics and for the variance of linear eigenvalue statistics are obtained. Moreover, the partition function logarithm up to the order O(1) is found.