Universality results for random matrices over finite local rings

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.

arXiv comment42 pages. Comments welcome! (Corrected typo on page 10 of preceding version.)