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Eigenvector statistics of the product of Ginibre matrices

Research output: Contribution to journalArticlepeer-review

Zdzislaw Burda, Bartłomiej Spisak, Pierpaolo Vivo

Original languageEnglish
JournalPHYSICAL REVIEW E
Volume95
Issue number2
DOIs
Accepted/In press2017
Published24 Feb 2017

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Abstract

We develop a method to calculate left-right eigenvector correlations of the product of m independent N×N complex Ginibre matrices. For illustration, we present explicit analytical results for the vector overlap for a couple of examples for small m and N. We conjecture that the integrated overlap between left and right eigenvectors is given by the formula O=1+(m/2)(N−1) and support this conjecture by analytical and numerical calculations. We derive an analytical expression for the limiting correlation density as N→∞ 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.

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