10 problems

Bapat–Sunder's conjecture. The largest eigenvalue of $F_A$ should satisfy

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define the Hadamard product…

Let $U$ be a Haar-random unitary matrix, and let $\operatorname{perm}(U)$ denote its permanent. The quantity $n!$ is the relevant Gaussian-scale second moment, and…

Let $X$ be a Gaussian random matrix, with the ensemble specified as needed among complex Ginibre, GOE, GUE, and real Ginibre matrices. Aaronson's conjecture. The random variable…

Let $\boldsymbol{\theta}$ be a matrix whose entries are independent and identically distributed non-negative real-valued random variables. The quantities…

Limiting permanent conjecture. The liminf is in fact a limit, namely

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For $A=[a_{i,j}]\in\mathcal{H}_n$, let $A(i,j)$ be obtained by deleting row $i$ and column…

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define…

Let $f_{312}(n)$ be the maximum permanent of an $n\times n$ 0-1 matrix avoiding the permutation pattern 312. Let $\mathcal{M}_n(\ast,\circ)$ be the set of $n\times n$ matrices obta…

Let $H$ be a Hadamard matrix of order $n$, and let … be the greatest exponent $e$ such that $2^e$ divides $n!$. Wanless's divisibility conjecture. The integer $2^{f(n)}$ divides…