5 problems

Non-backtracking eigenvector delocalization conjecture. Non-backtracking eigenvector delocalization holds when

Let $\mathbf{A}=\mathbf{P}+\mathbf{E}$ be the observed adjacency matrix, with rank parameter $r$, and suppose that Assumptions (deloc)–(moments) hold, except that the moment assump…

Let $A$ be an $n\times n$ matrix with i.i.d. subgaussian entries of zero mean and unit second absolute moment. For a unit eigenvector ${\bf v}=(v_1,\ldots,v_n)$, write $v_i^*$ for…

Let $v$ be uniformly distributed on the unit sphere in either $\mathbb{R}^n$ or $\mathbb{C}^n$. For the real case, there are constants $C,c>0$ such that, for every integer…

Let $H$ be a universal Wigner matrix with spread parameter $M$, and let $\mathbf{v}$ be an $\ell^2$-normalized eigenvector of $H$. The available result gives delocalization on a sc…