Universality for Cokernels of Dedekind Domain Valued Random Matrices

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 $\mathit{n}\times \mathit{n}$ matrices with entries valued in the domain. Previously, Wood found that when the entries of a random $\mathit{n}\times \mathit{n}$ integral matrix are not too concentrated modulo a prime, the asymptotic distribution (as $\mathit{n}\to \infty$) 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.