# On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries

## TL;DR

This paper investigates the asymptotic correlation functions of characteristic polynomials in non-Hermitian random matrices with independent entries, revealing their similarity to the Complex Ginibre Ensemble modulated by the fourth moment.

## Contribution

It demonstrates that the correlation functions of these matrices asymptotically match those of the Complex Ginibre Ensemble, scaled by a factor related to the fourth absolute moment of entries.

## Key findings

- Correlation functions resemble those of the Complex Ginibre Ensemble
- Behavior depends only on the fourth absolute moment of entries
- Results apply to matrices with independent entries

## Abstract

The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for the Complex Ginibre Ensemble up to a factor depending only on the fourth absolute moment of the common probability law of the matrix entries.