3 problems

Consider the one-dimensional Bernoulli displacement model with coupling parameter $\lambda$, integrated density of states $N$, and almost-sure spectrum $\Sigma_{\lambda}$. For…

Spectral-band conjecture. For every $\lambda\neq 0$,

Let $d\geq 2$, let $q\neq 0$ be sign-definite, and let $\omega^{\ast}$ denote the periodic configuration associated with the extremal spectral values $E_{min}$ and $E_{max}$. A per…