On the distribution of the determinant of the Gaussian unitary ensemble matrix

TL;DR

This paper characterizes the distribution of the determinant of Gaussian unitary ensemble matrices as a product of independent chi-distributed variables with specific parameters.

Contribution

It provides a novel representation of the determinant distribution for GUE matrices as a product of independent chi variables.

Findings

Determinant distribution expressed as a product of chi variables.

Parameters of chi variables follow a specific sequence.

Offers new insights into GUE matrix properties.

Abstract

The determinant of the Gaussian unitary ensemble matrix is show to be distributed as a product of independent chi random variables with parameters $1,3,3,5,5,\dots.$