3 problems

Let $H$ be a finite graph, let $\widetilde H$ be its universal cover, and let $H^n$ be a random uniform $n$-lift of $H$. Let $\sigma(H^n)$ denote the non-backtracking spectrum of…

Let $H$ be a finite graph and let $\widetilde H$ be its universal cover. Consider a large random lift of $H$, and separate its non-backtracking spectrum into the part arising from…

Let $H$ be a finite graph, called the base graph, and let $\pi\colon G\to H$ be a random lift of degree $n$. Eigenpairs of $A(H)$ pull back to eigenpairs of $A(G)$; call these old…