Wednesday, October 25, 2023 - 09:00 in ZOOM - Video Conference
Averages of products of characteristic polynomials and the law of real eigenvalues for the real Ginibre ensemble
A talk in the Bielefeld-Melbourne Seminar series by
Oleg Zaboronski
| Abstract: |
An elementary derivation of the Borodin-Sinclair-Forrester-Nagao
Pfaffian point process, which characterises the law of real eigenvalues for
the real Ginibre ensemble in the large matrix size limit, uses the averages of
products of characteristic polynomials. This derivation reveals a number of
interesting structures associated with the real Ginibre ensemble such as the
hidden symplectic symmetry of the statistics of real eigenvalues and an
integral representation for the $K$-point correlation function for any $K\in
\N$ in terms of an asymptotically exact integral over the symmetric space
$U(2K)/USp(2K)$.
Within the CRC this talk is associated to the project(s): B5, C6 |
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