4 problems

Universal fluctuation conjecture. The distribution of $Z$ is independent of $\vb{M}$ and $z$, satisfies

Pick-function conjecture. For every $n\in\mathbb{N}$, $f_n$ is a Pick function with Stieltjes representation

Finite-fourth-moment conjecture. The result of Theorem 1 should continue to hold with $\delta=0$.

Let $(G(z,t))_{z\in \mathbb{H},t\geqslant 0}$ be the solution of the evolution equation governing the continuum Stieltjes transform. Here $z$ lies in the upper half-plane and $t$ d…