The fluctuations of the mod p rank of triangular matrices
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913985917353984 |
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| author | Mészáros, András |
| author_facet | Mészáros, András |
| contents | We consider random lower triangular matrices such that the entries on and below the diagonal are i.i.d. copies of some $\mathbb{Z}$-valued random variable. We prove that the Sylow $p$-subgroups of the cokernels of these matrices have the same constant order fluctuations as that of the matrix products studied by Nguyen and Van Peski.
As a special case, we can describe the limiting fluctuations of the rank of lower triangular matrices over $\mathbb{F}_p$ with i.i.d. random entries on and below the diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fluctuations of the mod p rank of triangular matrices Mészáros, András Probability Combinatorics We consider random lower triangular matrices such that the entries on and below the diagonal are i.i.d. copies of some $\mathbb{Z}$-valued random variable. We prove that the Sylow $p$-subgroups of the cokernels of these matrices have the same constant order fluctuations as that of the matrix products studied by Nguyen and Van Peski. As a special case, we can describe the limiting fluctuations of the rank of lower triangular matrices over $\mathbb{F}_p$ with i.i.d. random entries on and below the diagonal. |
| title | The fluctuations of the mod p rank of triangular matrices |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2508.08788 |