Permanents of random matrices over finite fields

Fuente: arXiv
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Main Authors: Hunter, Zach, Kwan, Matthew, Sauermann, Lisa
Format: Preprint
Published: 2026
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author Hunter, Zach
Kwan, Matthew
Sauermann, Lisa
author_facet Hunter, Zach
Kwan, Matthew
Sauermann, Lisa
contents Fix a finite field $\mathbb F_q$ and let $A\in \mathbb F_q^{n\times n}$ be a uniformly random $n\times n$ matrix over $\mathbb F_q$. The asymptotic distribution of the determinant $\det(A)$ is well-understood, but the asymptotic distribution of the permanent $\operatorname{per}(A)$ is still something of a mystery. In this paper we make a first step in this direction, proving that $\operatorname{per}(A)$ is significantly more uniform than $\det(A)$.
format Preprint
id arxiv_https___arxiv_org_abs_2603_15856
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Permanents of random matrices over finite fields
Hunter, Zach
Kwan, Matthew
Sauermann, Lisa
Combinatorics
Computational Complexity
Probability
Fix a finite field $\mathbb F_q$ and let $A\in \mathbb F_q^{n\times n}$ be a uniformly random $n\times n$ matrix over $\mathbb F_q$. The asymptotic distribution of the determinant $\det(A)$ is well-understood, but the asymptotic distribution of the permanent $\operatorname{per}(A)$ is still something of a mystery. In this paper we make a first step in this direction, proving that $\operatorname{per}(A)$ is significantly more uniform than $\det(A)$.
title Permanents of random matrices over finite fields
topic Combinatorics
Computational Complexity
Probability
url https://arxiv.org/abs/2603.15856