Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911741536894976 |
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| author | Lee, Jungin Park, Sungjin |
| author_facet | Lee, Jungin Park, Sungjin |
| contents | In this paper, we prove universality of the distribution of the cokernels of a random $p$-adic matrix with inhomogeneously balanced columns. More precisely, let $u \ge 0$ be an integer and $A(n)$ be a random $n \times (n+u)$ matrix over $\mathbb{Z}_p$ whose $i$-th column is $α_n(i)$-balanced. We prove that if $\sum_{i=1}^{n+u} \exp(-εα_n(i)n) \to 0$ as $n \to \infty$ for every $ε>0$, then the cokernels of $A(n)$ converge in distribution, as $n \to \infty$, to the same limiting law as the cokernels of Haar-random $n \times (n+u)$ matrices over $\mathbb{Z}_p$. This extends a universality theorem of Nguyen and Wood to random $p$-adic matrices with inhomogeneously balanced columns. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_02180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns Lee, Jungin Park, Sungjin Number Theory Probability In this paper, we prove universality of the distribution of the cokernels of a random $p$-adic matrix with inhomogeneously balanced columns. More precisely, let $u \ge 0$ be an integer and $A(n)$ be a random $n \times (n+u)$ matrix over $\mathbb{Z}_p$ whose $i$-th column is $α_n(i)$-balanced. We prove that if $\sum_{i=1}^{n+u} \exp(-εα_n(i)n) \to 0$ as $n \to \infty$ for every $ε>0$, then the cokernels of $A(n)$ converge in distribution, as $n \to \infty$, to the same limiting law as the cokernels of Haar-random $n \times (n+u)$ matrices over $\mathbb{Z}_p$. This extends a universality theorem of Nguyen and Wood to random $p$-adic matrices with inhomogeneously balanced columns. |
| title | Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2606.02180 |