Paper
Random integral matrices and the Cohen Lenstra Heuristics
Authors
Melanie Matchett Wood
Abstract
We prove that given any , random integral matrices with independent entries that lie in any residue class modulo a prime with probability at most have cokernels asymptotically (as ) distributed as in the distribution on finite abelian groups that Cohen and Lenstra conjecture as the distribution for class groups of imaginary quadratic fields. This is a refinement of a result on the distribution of ranks of random matrices with independent entries in . This is interesting especially in light of the fact that these class groups are naturally cokernels of square matrices. We also prove the analogue for matrices.