Abstract
We develop a method to calculate left-right eigenvector correlations of the product of independent complex Ginibre matrices. For illustration, we present explicit analytical results for the vector overlap for a couple of examples for small and . We conjecture that the integrated overlap between left and right eigenvectors is given by the formula and support this conjecture by analytical and numerical calculations. We derive an analytical expression for the limiting correlation density as for the product of Ginibre matrices as well as for the product of elliptic matrices. In the latter case, we find that the correlation function is independent of the eccentricities of the elliptic laws.
1 More- Received 1 November 2016
DOI:https://doi.org/10.1103/PhysRevE.95.022134
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