3 problems

Fix an integer $d\ge 3$, and let $A^{(d)}_n$ be uniformly drawn from the set $\mathcal{A}_{n,d}$ of adjacency matrices of $d$-regular directed graphs on $n$ vertices. Let…

Let $A_n$ be a random regular digraph matrix, meaning a uniformly random element of $\mathop{\mathrm{M}}_n(d)$, where $\mathop{\mathrm{M}}_n(d)$ is the set of $n\times n$ zero-one…

Let $M$ be a uniform random element of the set of $n\times n$ zero-one matrices with every row and column sum equal to $d$. Polynomial singularity conjecture. There are absolute co…