6 problems

Let $f$ be in the Laguerre--Pólya class and satisfy the regular-variation condition on its roots. Let … and set $\rho=\frac{1}{\alpha}-1$. Write $\mu_p$ for the empirical root dist…

Let $n\geq 3$ and consider extremizers of the $p$-Stam inequality among normalized monic real-rooted polynomial pairs $(f,g)$ of degree $n$; write $d_{PQ}$ for their pair mismatch…

For each $n\geq 3$, consider the $p$-Stam inequality for monic real-rooted pairs of degree $n$, with critical exponent denoted by $p^*$. $p$-Stam phase transition conjecture. For a…

Let $n\geq 3$, let $h\in\mathbb{R}^n$ be the normalized Hermite root vector, and define … Let $W=\mathbf{1}^\perp=\{u\in\mathbb{R}^n:u^\top\mathbf{1}=0\}$ be the mean-zero subspace…

Let $p_d$ be a monic polynomial of degree $d$ with non-negative real roots … Let $\mu\in\mathcal{P}_{+,c}$, and suppose that the empirical root distributions of $p_d$ converge weak…

Rank-two permanent inequality. For any matrix $T$ with rank at most $2$,