2 problems

Multiplicative-convolution conjecture. The measure $\mu_1\cdot \mu_2 \dotsb \mu_k$ is absolutely continuous with respect to Lebesgue measure.

For each $d\geq 1$, let $\Phi_d$ be the limiting-polynomial map associated with finite free multiplicative convolution, and let $\Phi$ be the map characterized by the free multipli…