3 problems

Borderline Lifshits-tail conjecture. As $E\downarrow0$,

Let $p$ be the Bernoulli parameter, let $\beta^{-1}(n)$ denote the decreasing sequence appearing in the model, and let $I_{p,\zeta}(x)$ be the integrated density of states at disor…

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