The Sixth Moment of Random Determinants
Combinatorics
2023-02-28 v2 Probability
Abstract
In this paper, we determine the sixth moment of the determinant of an asymmetric random matrix where the entries are drawn independently from an arbitrary distribution with mean . Furthermore, we derive the asymptotic behavior of the sixth moment of the determinant as the size of the matrix tends to infinity.
Cite
@article{arxiv.2206.11356,
title = {The Sixth Moment of Random Determinants},
author = {Dominik Beck and Zelin Lv and Aaron Potechin},
journal= {arXiv preprint arXiv:2206.11356},
year = {2023}
}
Comments
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