Permanents of random matrices over finite fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918391832379392 |
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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 |