11 problems

Singularity-obstruction conjecture. If $c\in(0,1/2)$ is fixed and

Let $Q_n$ be a random matrix whose independent rows are chosen uniformly from the vectors in $\{0,1\}^n$ having sum exactly $\lfloor n/2\rfloor$. Nguyen's conjecture. … This model…

Litvak–Tikhomirov conjecture. Then

Let $B_n(p)$ be an $n\times n$ random matrix with independent and identically distributed Bernoulli entries of mean $p$, and let $q_n(p)=\mathbb{P}[B_n(p)\text{ is singular}]$. Loc…

Weiss's singularity conjecture.

Let $M_n$ be a random $n\times n$ symmetric matrix whose upper-diagonal entries are independent Bernoulli random variables taking the values $1$ and $-1$ with probability $1/2$ eac…

Let $M_n^{\mathrm{sym}}$ be a random symmetric matrix whose upper-diagonal entries are iid Bernoulli variables, and let $p_n^{\mathrm{sym}}$ denote its probability of being singula…

Let $M_n$ be an $n\times n$ random matrix with iid Bernoulli entries, and let $p_n={\mathbf P}(M_n\text{ is singular})$. Erdős–Kahn–Komlós–Szemerédi conjecture. … This is described…

Let $n$ be even, and let $Q_n$ be a random $n$ by $n$ $(0,1)$ matrix whose rows are independent vectors with exactly $n/2$ zero components. Fixed-row-sum singularity probability co…

Let $A_n$ be an $n$ by $n$ random matrix whose entries are independent Bernoulli random variables. Komlós' singularity probability conjecture. The probability that $A_n$ is singula…

Let $M=M_n$ be a random $n\times n$ Bernoulli matrix, let $S$ be the event that $M$ is singular, and let $\lambda(1),\lambda(2),\ldots$ be any enumeration of the set of novel integ…