Distribution of the cokernels of determinantal row-sparse matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914236977905664 |
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| author | Lee, Jungin Yu, Myungjun |
| author_facet | Lee, Jungin Yu, Myungjun |
| contents | We study the distribution of the cokernels of random row-sparse integral matrices $A_n$ according to the determinantal measure from a structured matrix $B_n$ with a parameter $k_n \ge 3$. Under a mild assumption on the growth rate of $k_n$, we prove that the distribution of the $p$-Sylow subgroup of the cokernel of $A_n$ converges to that of Cohen--Lenstra for every prime $p$. Our result extends the work of A. Mészáros which established convergence to the Cohen--Lenstra distribution when $p \ge 5$ and $k_n=3$ for all positive integers $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distribution of the cokernels of determinantal row-sparse matrices Lee, Jungin Yu, Myungjun Probability Combinatorics Number Theory We study the distribution of the cokernels of random row-sparse integral matrices $A_n$ according to the determinantal measure from a structured matrix $B_n$ with a parameter $k_n \ge 3$. Under a mild assumption on the growth rate of $k_n$, we prove that the distribution of the $p$-Sylow subgroup of the cokernel of $A_n$ converges to that of Cohen--Lenstra for every prime $p$. Our result extends the work of A. Mészáros which established convergence to the Cohen--Lenstra distribution when $p \ge 5$ and $k_n=3$ for all positive integers $n$. |
| title | Distribution of the cokernels of determinantal row-sparse matrices |
| topic | Probability Combinatorics Number Theory |
| url | https://arxiv.org/abs/2505.11700 |