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arXiv · 2403.09909

Cokernels of random matrix products and flag Cohen--Lenstra heuristic

Yifeng Huang
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Abstract

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.

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Yifeng Huang. 2024-03-14. Cokernels of random matrix products and flag Cohen--Lenstra heuristic. https://arxiv.org/abs/2403.09909

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