The Sixth Moment of Random Determinants

Abstract

In this paper, we determine the sixth moment of the determinant of an asymmetric $n\times n$ random matrix where the entries are drawn independently from an arbitrary distribution $\Omega$ with mean $0$. Furthermore, we derive the asymptotic behavior of the sixth moment of the determinant as the size of the matrix tends to infinity.

This update contains several additional results, namely a generating function for $f_6(n)$, a simpler formula for $f_6(n)$, the asymptotic behavior of $f_6(n)$ as $n$ goes to infinity, and a generalization of these results to the case when $\Omega$ has a nonzero third moment