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arXiv · 2301.09196

Universality for Cokernels of Dedekind Domain Valued Random Matrices

Eric Yan
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Abstract

We use the moment method of Wood to study the distribution of random finite modules over a countable Dedekind domain with finite quotients, generated by taking cokernels of random $n\times n$ matrices with entries valued in the domain. Previously, Wood found that when the entries of a random $n\times n$ integral matrix are not too concentrated modulo a prime, the asymptotic distribution (as $n\to\infty$) of the cokernel matches the Cohen and Lenstra conjecture on the distribution of class groups of imaginary quadratic fields. We develop and prove a condition that produces a similar universality result for random matrices with entries valued in a countable Dedekind domain with finite quotients.

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Eric Yan. 2023-01-22. Universality for Cokernels of Dedekind Domain Valued Random Matrices. https://arxiv.org/abs/2301.09196

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