Sharp threshold for universality of cokernels of classical random matrix models over the $p$-adic integers

Jiwan Jung, Jungin Lee, Myungjun Yu

We prove that $\frac{\log n}{n}$ is the sharp threshold for universality of the distribution of cokernels of random matrices over ${\mathbb{Z}}_p$. More precisely, let $α_n = \frac{c…