Random $p$-adic matrices with fixed zero entries and the Cohen--Lenstra distribution

Dong Yeap Kang, Jungin Lee, Myungjun Yu

In this paper, we study the distribution of the cokernels of random $p$-adic matrices with fixed zero entries. Let $X_n$ be a random $n\times n$ matrix over ${\mathbb{Z}}_p$ in whic…