The distribution of the cokernel of a polynomial evaluated at a random integral matrix

Gilyoung Cheong, Myungjun Yu

Given a prime $p$, let $P(t)$ be a non-constant monic polynomial in $t$ over the ring ${\mathbb{Z}}_p$ of $p$-adic integers. Let $X_n$ be an $n\times n$ random matrix over $\mat…