The Minkowski inequality for the discriminant of finite free convolutions

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 inequality.

$$\operatorname{Dis}(p \boxplus_d q)^{\frac{1}{\binom{d}{2}}} \geq \operatorname{Dis}(p)^{\frac{1}{\binom{d}{2}}}+\operatorname{Dis}(q)^{\frac{1}{\binom{d}{2}}}$$

Equality holds only for generalized Hermite polynomials. This is presented as a broader inequality related to the entropy and log-discriminant of a polynomial; the supplied text does not establish whether the inequality or its equality characterization is proved or remains open.