Cohen–Lenstra heuristics and random matrix theory over finite fields

Abstract

Abstract. Let g be a random element of a finite classical group G, and let λ z-1(g) denote the partition corresponding to the polynomial z - 1 in the rational canonical form of g. As the rank of G tends to infinity, λ z-1(g) tends to a partition distributed according to a Cohen–Lenstra type measure on partitions. We give sharp upper and lower bounds on the total variation distance between the random partition λ z-1(g) and the Cohen–Lenstra type measure.