Full Dysonian dynamics of the complex Ginibre ensemble

Abstract

We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degrees of freedom. We solve the accompanying Smoluchowski-Fokker-Planck equation valid for any initial matrix. We derive evolution equations for the averaged extended characteristic polynomial and for a class of $k$-point eigenvalue correlation functions. From the latter we obtain a novel formula for the eigenvector correlation function which we inspect for Ginibre and spiric initial conditions and obtain macro- and microscopic limiting laws.

Locations

• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
• DataCite API - View
• Journal of Physics A Mathematical and Theoretical - View