Universality results for random matrices over finite local rings

TL;DR

This paper establishes universality results for the cokernel and other invariants of random matrices over finite local rings, using the Lindeberg replacement technique instead of the traditional moment method.

Contribution

It introduces a new approach employing the Lindeberg replacement technique to prove universality for matrix invariants over finite local rings, extending beyond cokernels.

Findings

Universality results for cokernels of random matrices over finite local rings.

Extension of universality to invariants like span and determinant.

Use of Lindeberg replacement technique instead of moment method.

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.