Correlations of Eigenvectors for Non-Hermitian Random-Matrix Models

TL;DR

This paper derives a general relation linking eigenvector correlations to the spectral Green's function in non-Hermitian random matrices, validated through numerical experiments across various models.

Contribution

It introduces a universal relation between eigenvector correlators and Green's functions for non-Hermitian matrices, expanding theoretical understanding.

Findings

The relation holds in the large-N limit.

Numerical results agree with theoretical predictions.

Applicable to multiple non-Hermitian models.

Abstract

We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix models and show that the outcome is in good agreement with numerical results.