Large corank of dense random regular digraphs

Huaijin Liang, Kexin Yu, Tingzhou Yu

Let $1\le k\le n$ and let $A$ be the adjacency matrix of a uniformly random $d$-regular directed graph on $n$ vertices. Suppose that $\lambda n\le d\le (1-\lambda )n$ for a fixed $0<\lambda \le 1/2$.…