Cokernels of random matrix products and flag Cohen--Lenstra heuristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910368143507456 |
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| author | Huang, Yifeng |
| author_facet | Huang, Yifeng |
| contents | In [NVP22], Nguyen and Van Peski raised the question of whether the surjective flag of $\mathbb Z_p$-modules modeled by $\mathrm{cok}(M_1\cdots M_k)\twoheadrightarrow \dots\twoheadrightarrow \mathrm{cok}(M_1)$ for independent random matrices $M_1,\dots,M_k\in \mathrm{Mat}_n(\mathbb Z_p)$ satisfies the Cohen--Lenstra heuristic. We answer the question affirmatively when $M_1,\dots,M_k$ follow the Haar measure, and our proof demonstrates how classical ideas in Cohen--Lenstra heuristic adapt naturally to the flag setting. We also prove an analogue for non-square matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cokernels of random matrix products and flag Cohen--Lenstra heuristic Huang, Yifeng Number Theory Combinatorics Probability In [NVP22], Nguyen and Van Peski raised the question of whether the surjective flag of $\mathbb Z_p$-modules modeled by $\mathrm{cok}(M_1\cdots M_k)\twoheadrightarrow \dots\twoheadrightarrow \mathrm{cok}(M_1)$ for independent random matrices $M_1,\dots,M_k\in \mathrm{Mat}_n(\mathbb Z_p)$ satisfies the Cohen--Lenstra heuristic. We answer the question affirmatively when $M_1,\dots,M_k$ follow the Haar measure, and our proof demonstrates how classical ideas in Cohen--Lenstra heuristic adapt naturally to the flag setting. We also prove an analogue for non-square matrices. |
| title | Cokernels of random matrix products and flag Cohen--Lenstra heuristic |
| topic | Number Theory Combinatorics Probability |
| url | https://arxiv.org/abs/2403.09909 |