A phase transition for the cokernels of random band matrices over the p-adic integers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916367613034496 |
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| author | Mészáros, András |
| author_facet | Mészáros, András |
| contents | Let $\mathbf{B}_n$ be an $n\times n$ Haar-uniform band matrix over $\mathbb{Z}_p$ with band width $w_n$. We prove that $\text{cok}(\mathbf{B}_n)$ has Cohen-Lenstra limiting distribution if and only if \[\lim_{n\to\infty} \left(w_n-\log_p(n)\right)=+\infty.\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A phase transition for the cokernels of random band matrices over the p-adic integers Mészáros, András Probability Combinatorics Let $\mathbf{B}_n$ be an $n\times n$ Haar-uniform band matrix over $\mathbb{Z}_p$ with band width $w_n$. We prove that $\text{cok}(\mathbf{B}_n)$ has Cohen-Lenstra limiting distribution if and only if \[\lim_{n\to\infty} \left(w_n-\log_p(n)\right)=+\infty.\] |
| title | A phase transition for the cokernels of random band matrices over the p-adic integers |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2408.13037 |