4 problems

Let $A_n$ be a uniformly random element of the set of adjacency matrices of $d$-regular directed graphs on $n$ vertices, and let $\frac{1}{\sqrt d}A_n$ have empirical spectral dist…

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…

Dense singularity conjecture. There are constants $C,c>0$ depending only on $\pe_0$ such that