Distribution of cokernels of ($n$+$u$) $\times$ $n$ matrices over ${\mathbb{Z}}_p$

Abstract

Let $n,u\ge 0$, $M$ be a ($n$+$u$) $\times$ $n$ matrices over ${\mathbb{Z}}_p$, and $G$ be a finite abelian p-group group. We find that the probability that the cokernel of $M$ is isomorphic to ${\mathbb{Z}}_p^u\oplus G$ as $n$ goes to infinity is exactly what is expected from Cohen-Lenstra heuristics for the classical case when $u$ is negative.

7 pages

References in corpus (1)

• The distribution of sandpile groups of random graphs

Cited by in corpus (1)

• Random Partitions and Cohen-Lenstra Heuristics