4 problems

Conditional non-degeneracy conjecture. For fixed $k\geq 2$, the conditional distribution of $\alpha(\mathcal W_{d+k,d})$ converges weakly as $d\to\infty$ to a limit law not concent…

Rare-spike limit conjecture. The sequence of measures $(\mu_d)_{d\in\mathbb N}$ converges weakly to a non-trivial limit.

Weak-limit conjecture. As $d\to\infty$, the random variables

Higher-moment asymptotics. For every fixed $k\in \{2,3,\ldots\}$, we have