Ornstein–Uhlenbeck diffusion of hermitian and non-hermitian matrices—unexpected links
Ornstein–Uhlenbeck diffusion of hermitian and non-hermitian matrices—unexpected links
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 …