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arXiv · 1804.09740

Full Dysonian dynamics of the complex Ginibre ensemble

Jacek Grela·Piotr Warchoł
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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.

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Jacek Grela, Piotr Warchoł. 2018-04-25. Full Dysonian dynamics of the complex Ginibre ensemble. https://doi.org/10.1088/1751-8121%2Faadd54

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