%0 Journal Article
%T Ornstein-Uhlenbeck diffusion of hermitian and non-hermitian matrices - unexpected links
%A Jean-Paul Blaizot
%A Jacek Grela
%A Maciej A. Nowak
%A Wojciech Tarnowski
%A Piotr Warcho£¿
%J Statistics
%D 2015
%I arXiv
%X We compare the Ornstein-Uhlenbeck process for the Gaussian Unitary Ensemble to its non-hermitian counterpart - for the complex Ginibre ensemble. We exploit the mathematical framework based on the generalized Green's functions, which involves a new, hidden complex variable, in comparison to the standard treatment of the resolvents. This new variable turns out to be crucial to understand the pattern of the evolution of non-hermitian systems. The new feature is the emergence of the coupling between the flow of eigenvalues and that of left/right eigenvectors. We analyze local and global equilibria for both systems. Finally, we highlight some unexpected links between both ensembles.
%U http://arxiv.org/abs/1512.06599v1