2015/12/31 by Jean-Paul Blaizot, Jacek Grela, Maciej A. Nowak +2 · 6 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Computer science #Coupling (piping) #Dependency (UML) #Eigenvalues and eigenvectors #Feature (linguistics) #Gaussian #Hermitian matrix #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Unitary state #Variable (mathematics) #math-ph #math.MP #math.PR #nlin.CD
paper · pdf · doi:10.1088/1742-5468/2016/05/054037
published in Journal of Statistical Mechanics Theory and Experiment 2016(5), 054037 (Institute of Physics) · 21 pages, 4 figures, submitted to J. Stat. Phys
arxiv created 2016/01/04 · openalex publication_date 2016/05/20 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.