2 problems

Random matching decomposition conjecture. The event that the disjoint union belongs to $A_n$ holds with high probability if and only if the event that a uniform random $d$-regular…

Let $L\geq 2$, let $G=\mathbb{Z}/L$ (modulo $L$), and let $\Psi_1$ consist of the single frequency $j\mapsto\exp(2\pi i j/L)$. Let $\lambda^*$ denote the boundary below which the s…