2 problems

Let $p$ and $q$ be degree-$d$ polynomials, let $p\boxplus_d q$ denote their finite free convolution, and let $\operatorname{Dis}(p)$ denote the discriminant of $p$. Minkowski inequ…

Let $p$ and $q$ be real-rooted polynomials of degree $d$, and let $\f$ be in $C^{4}(\mathbb{R})$ with $f^{(4)}\geq 0$. Write $\mu_p$ and $\mu_q$ for the probability measures assign…