Analysis Seminar: Ron Rosenthal (Technion) "Eigenvector correlation in the complex Ginibre ensemble"

Title: Eigenvector correlation in the complex Ginibre ensemble
Abstract:
The complex Ginibre ensemble is a non-Hermitian random matrix on $\mathbb{C}^N$ with i.i.d. complex Gaussian entries normalized to have mean zero and variance $1/N$. Unlike the Gaussian unitary ensemble, for which the eigenvectors are orthogonal, the geometry
of the eigenbases of the Ginibre ensemble are not particularly well understood.
We will discuss a some results regarding the analytic and algebraic structure of eigenvector correlations in this matrix ensemble. In particular, we uncover an extended
algebraic structure which describes the asymptotic behavior (as N goes to infinity) of
these correlations. Our work extends previous results of Chalker and Mehlig [CM98],
in which the correlation for pairs of eigenvectors was computed.
Based on a joint work with Nick Crawford

Date: 

Wed, 05/12/2018 - 12:00 to 13:00