Regularization of Non-Normal Matrices by Gaussian Noise.

We consider the regularization of matrices M^N in Jordan form by additive Gaussian noise N^-γ G^N, where G^N is a matrix of i.i.d. standard Gaussians and γ > 1/2 so that the operator norm of the additive noise tends to 0 with N. Under mild conditions on the structure of M^N, we evaluate the limit of the empirical measure of eigenvalues of M^N + N^-γ GN and show that it depends on γ , in contrast with the case of a single Jordan block. [ABSTRACT FROM AUTHOR]