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arXiv · 2601.10821

Universality results for random matrices over finite local rings

Nikita Lvov
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Abstract

Let $R$ be a finite local ring. We prove a quantitative universality statement for the cokernel of random matrices with i.i.d. entries valued in $R$. Rather than use the moment method, we use the Lindeberg replacement technique. This approach also yields a universality result for several invariants that are finer than the cokernel, such as the span and the determinant.

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Nikita Lvov. 2026-01-15. Universality results for random matrices over finite local rings. https://arxiv.org/abs/2601.10821

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