Wednesday, April 18, 2018 - 16:15 in V3-201
On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
A talk in the Seminar Zufallsmatrizen series by
Yan Fyodorov from King’s College London
| Abstract: |
I will present a method of studying the joint probability density (JPD) of an eigenvalue and the associated ’non-orthogonality overlap factor’ (also known as the condition number) of the left and right eigenvectors for non-selfadjoint Gaussian random matrices.
First I derive the exact finite-N expression in the case of real eigenvalues and the associated nonorthogonality factors in the real Ginibre ensemble, and then analyse its ‘bulk’ and ‘edge’ scaling limits. The ensuing distributions are maximally heavy-tailed, so that all integer moments beyond normalization are divergent.
Then I present results for a complex eigenvalue and the associated non-orthogonality factor in the complex Ginibre ensemble complementing recent studies by P. Bourgade & G. Dubach. The presentation will be mainly based on the paper arXiv: 1710.04699 and a joint work with Jacek Grela and Eugene Strahov arXiv: 1711.07061.
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