title: Eigenvector statistics of the product of Ginibre matrices.
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.
authors.affiliation: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland.
authors.forename: Zdzisław
authors.initials: Z
authors.lastname: Burda
authors.affiliation: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland.
authors.forename: Bartłomiej J
authors.initials: BJ
authors.lastname: Spisak
authors.affiliation: Department of Mathematics, King's College London, Strand WC2R 2LS, London, United Kingdom.
authors.forename: Pierpaolo
authors.initials: P
authors.lastname: Vivo