Wednesday, November 8, 2023 - 09:00 in ZOOM - Video Conference
On the self-overlap between left and right eigenvectors in the real Ginibre ensemble
A talk in the Seminar Zufallsmatrizen series by
Mark Crumpton from King's College London
| Abstract: |
Non-normal matrices are much more sensitive to additive perturbations as
compared to their normal counterparts. This sensitivity can be quantified ap-
pealing to the so-called self-overlap of their left and right eigenvectors. We
study the first moment of the self-overlap for complex eigenvalues of $N \times N$
matrices in the real Ginibre ensemble. As part of this talk, we provide an
overview of the techniques pertinent to our studies, such as incomplete
Schur decomposition and Grassmann integration. The derived expression for
the first moment is valid for finite size $N$ of matrices, however we are mainly
interested in its large-$N$ asymptotic behaviour. This is calculated in three
different regions of the complex plane with different density of eigenvalues:
the spectral bulk, the spectral edge and a region of eigenvalue depletion close
to the real line. New results in this talk are compared to existing results for
the complex Ginibre ensemble and verified using numerical simulation.
Please contact Lucas Hackl (Lucas.Hackl@unimelb.edu.au) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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