5 problems

Rank-resilience conjecture. With probability $1-o(1)$,

Let $Q_{n,d}$ be the adjacency matrix of a uniformly random simple $d$-regular graph on $n$ vertices. Random regular nonsingularity conjecture. For every $d\ge 3$, $Q_{n,d}$ is alm…

Let $M$ be a $\{-1,1\}$ matrix. Call $M$ good if every matrix obtained by independently switching any subset of its diagonal entries is nonsingular. Let $M_n$ be a random…

For a $\{-1,1\}$ matrix $M$, let $\operatorname{Res}(M)$ be the minimum number of entries that must be switched from $1$ to $-1$ or vice versa in order to make $M$ singular. Let…

Stubborn-matrix conjecture. With probability $1-o(1)$, $M_n$ is stubborn.